Matrices
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This document defines and provides examples of different types of matrices including upper triangular, lower triangular, transpose, symmetric, and inverse matrices. It also describes common operations that can be performed on matrices such as addition, subtraction, scalar multiplication, and matrix multiplication. These operations have specific properties like associativity, neutral elements, and distributivity.
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The document provides an introduction to matrix operations including addition, subtraction, multiplication, and determinants. It defines what a matrix is and how they are represented and sized. It then explains how to perform addition and subtraction of matrices by adding or subtracting the corresponding entries. Matrix multiplication is defined as being possible only when the number of columns of the first matrix equals the rows of the second. Determinants are explained as being unique to square matrices, and formulas are given for finding the determinants of 2x2 and 3x3 matrices. Homework problems are assigned involving computing various matrix operations.Matrices
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matrices
The beginnings of matrices goes back to the second century BC although traces can be seen back to the fourth century BC. However it was not until near the end of the 17th Century that the ideas reappeared and development really got underway.
It is not surprising that the beginnings of matrices and determinants should arise through the study of systems of linear equations. The Babylonians studied problems which lead to simultaneous linear equations and some of these are preserved in clay tablets which survive.MATRICES AND ITS TYPE
MATRICES AND ITS TYPEHimanshu Negi
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The document presents information on matrices and their types. It defines a matrix as an arrangement of numbers, symbols or expressions in rows and columns. It discusses different types of matrices including row matrices, column matrices, square matrices, rectangular matrices, diagonal matrices, scalar matrices, unit/identity matrices, symmetric matrices, complex matrices, hermitian matrices, skew-hermitian matrices, orthogonal matrices, unitary matrices, and nilpotent matrices. It provides examples and definitions for hermitian matrices, orthogonal matrices, idempotent matrices, and nilpotent matrices. The presentation was given by Himanshu Negi on matrices and their types.Matrix and its applications by mohammad imran
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This document provides an overview of matrix mathematics concepts. It discusses how matrices are useful in engineering calculations for storing values, solving systems of equations, and coordinate transformations. The outline then reviews properties of matrices and covers various matrix operations like addition, multiplication, and transposition. It also defines different types of matrices and discusses determining the rank, inverse, eigenvalues and eigenvectors of matrices. Key matrix algebra topics like solving systems of equations and putting matrices in normal form are summarized.Matrices
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A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrixIntroduction to matices
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InshahAllah i will upload many other simple slides on various disciplines. Suggest and comment me necessary. presentation on matrix
presentation on matrixNikhi Jain
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This document defines and provides examples of different types of matrices:
- Matrices are arrangements of elements in rows and columns represented by symbols.
- Types include row matrices, column matrices, square matrices, null matrices, identity matrices, diagonal matrices, scalar matrices, triangular matrices, transpose matrices, symmetric matrices, skew matrices, equal matrices, and algebraic matrices.
- Algebraic matrix operations include addition, subtraction, and multiplication where the matrices must be of the same order.matricesMrtices
matricesMrticesYourskill Tricks
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This document provides an overview of matrices including:
- Definitions of matrices, order of matrices, and compact matrix form
- Matrix multiplication and checking compatibility of matrices
- Determinants, adjoints, and inverses of matrices
- Methods for solving systems of equations using matrices including Gauss-Jordan elimination and Cramer's rule
The document also provides brief biographies of James Joseph Sylvester and Arthur Cayley, two mathematicians who made important contributions to the field of matrices.Project business maths
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The history and development of matrix theory is summarized as follows:
1) The term "matrix" was introduced in 1850 by James Joseph Sylvester to describe rectangular arrays of numbers or expressions arranged in rows and columns.
2) The founder of modern matrix theory is considered to be Arthur Cayley, who in the 1850s introduced concepts such as inverse matrices and matrix multiplication.
3) Important developments in matrix theory continued throughout the 19th and 20th centuries, including the discovery by Arthur Cayley and William Hamilton of unique properties of matrices.Matrices
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This document defines and describes various types of matrices. It defines a matrix as a rectangular array of numbers or functions with m rows and n columns referred to as an m x n matrix. It then lists and defines the following types of matrices: row matrix, column matrix, null matrix, rectangular matrix, square matrix, diagonal matrix, scalar matrix, unit matrix, symmetric matrix, and skew-symmetric matrix. It provides examples of each type of matrix and their general syntax.Notes of Matrices and Determinants
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This document covers matrices, determinants, and their properties. Some key points:
- A matrix is a rectangular arrangement of numbers. The order of a mn matrix is defined by its m rows and n columns.
- A square matrix is symmetric if it is equal to its transpose, and skew-symmetric if it is equal to the negative of its transpose.
- The determinant of a square matrix provides a number associated with the matrix, denoted |A| or detA.
- Properties of determinants include that the value does not change under row/column interchange operations, and that multiplying a row/column by a constant k multiplies the determinant by k.MATRICES
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This document defines and describes different types of matrices including:
- Upper and lower triangular matrices
- Determinants which are scalars obtained from products of matrix elements according to constraints
- Band matrices which are sparse matrices with nonzero elements confined to diagonals
- Transpose matrices which exchange the rows and columns of a matrix
- Inverse matrices which when multiplied by the original matrix produce the identity matrixMatrices y determinants
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This document discusses matrices and their properties. It defines a matrix as a rectangular array of numbers arranged in rows and columns. It describes several types of matrices including line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also explains common operations that can be performed on matrices such as addition, subtraction, scalar multiplication, and multiplication. Key properties of these matrix operations are provided.Matrices 1
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This document provides an overview of matrices and basic matrix operations. It discusses what matrices are, how to perform operations like addition, multiplication, and taking the transpose. It also covers special types of matrices like diagonal, triangular, and identity matrices. It explains how to calculate the determinant of a 2x2 matrix and find the inverse of a 2x2 matrix using the determinant. The goal is for the reader to understand matrices, common operations, and how to calculate the determinant and inverse of a 2x2 matrix after reviewing this material.MATRICES
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This document provides an overview of matrices and matrix operations. It begins by stating the objectives of understanding matrix characteristics, applying basic matrix operations, knowing inverse matrices up to 3x3, and solving simultaneous linear equations up to 3 variables. It then defines what a matrix is, discusses matrix dimensions and types of matrices. The document outlines various matrix operations including addition, subtraction, multiplication and scalar multiplication. It provides examples of how to perform these operations. It also covers the transpose of a matrix and inverse matrices.INTRODUCTION TO MATRICES, TYPES OF MATRICES, 
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Matrices can be added, subtracted, and multiplied under certain conditions.
Addition and subtraction require matrices to be the same size.
Matrix multiplication requires the number of columns of the first matrix to equal the number of rows of the second matrix.
Matrices can also be multiplied by scalars.Matrix.
Matrix.Awais Bakshy
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The document defines and provides examples of different types of matrices, including:
- Square matrices, where the number of rows equals the number of columns.
- Rectangular matrices, where the number of rows does not equal the number of columns.
- Row matrices, with only one row.
- Column matrices, with only one column.
- Null or zero matrices, with all elements equal to zero.
- Diagonal matrices, with all elements equal to zero except those on the main diagonal.
The document also discusses transpose, adjoint, and addition of matrices.Matrices And Determinants
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Matrices are widely used in business, economics, and other fields. They allow problems to be represented with distinct finite numbers rather than infinite gradations as in calculus. Sociologists, demographers, and economists use matrices to study groups, populations, industries, and social accounting. [/SUMMARY]Introduction of matrix
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The document defines various types of matrices including row vectors, column vectors, submatrices, square matrices, triangular matrices, diagonal matrices, identity matrices, zero matrices, and diagonally dominant matrices. It provides examples of each type of matrix. It also discusses when two matrices are considered equal, which is when they have the same size and corresponding elements are equal.Matrices - multiplication of matrices 
Matrices - multiplication of matrices LiveOnlineClassesInd
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- The document discusses how to multiply matrices, including defining when multiplication is valid based on the number of columns and rows of the matrices.
- It provides an example of multiplying two matrices, showing the step-by-step process of multiplying corresponding elements and summing them.
- It also discusses properties of matrix multiplication, including associativity, distributivity, and the existence of an identity matrix.
- Examples are provided to illustrate verifying these properties by calculating different matrix multiplications.M a t r i k s
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1. The document discusses various types and operations of matrices including transpose, similarity, inverse, and determinant of matrices.
2. It also discusses using matrices to solve systems of linear equations by finding the inverse of the coefficient matrix or calculating the determinant.
3. The key matrix concepts covered are matrix notation, types of matrices, matrix addition/subtraction, multiplication, and using matrices to represent and solve linear systems.Matrix and it's application 
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The m x n matrix with all entries of zero is denoted by _ , for a matrix A of size m x n, we have:
matrices and function ( matrix)
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This document is an introduction to matrices presented by Reza At-Tanzil of the Department of Pharmacy at Comilla University. It defines what a matrix is, describes different types of matrices including column/row matrices, rectangular matrices, square matrices, diagonal matrices, identity matrices, null matrices, and scalar matrices. It also covers matrix operations such as matrix multiplication, transpose of a matrix, symmetric matrices, inverse of a matrix, and adjoint matrices.Determinants
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The document discusses determinants and their properties. It defines determinants as representing single numbers obtained by multiplying and adding matrix elements in a special way. It then provides formulas for calculating determinants of matrices of order 1, 2 and 3. It also outlines several properties of determinants, such as how interchanging rows/columns, multiplying rows by constants, and adding rows affects the determinant. Finally, it discusses how determinants are used to determine whether systems of linear equations are consistent or inconsistent.Lesson 1 - Introduction to Matrices
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The document defines key terms and concepts relating to matrices. It explains that a matrix is a two-dimensional array with rows and columns used to organize data. Matrices allow for simple display of data with non-essential information removed. They have various applications including graphic design and solving equations. The document defines order, elements, and notation for referring to entries in a matrix. It provides examples for stating the order, values, and positions of elements in matrices. Finally, it describes special types of matrices such as column, row, square, and triangular matrices as well as properties like the transpose and leading diagonal.Matrices
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油
This document defines and explains different types of matrices:
- Upper and lower triangular matrices have zeros above or below the main diagonal of a square matrix.
- The determinant of a matrix is a scalar value obtained from the products of the matrix's elements according to certain constraints.
- A banded matrix is a sparse matrix with nonzero elements confined to a diagonal band around the main diagonal.
- The transpose of a matrix exchanges the rows and columns of the original matrix.
- For matrix multiplication to be defined, the number of columns of the left matrix must equal the number of rows of the right matrix.Basic concepts. Systems of equations
Basic concepts. Systems of equationsjorgeduardooo
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This document defines and provides examples of different types of matrices:
- Upper and lower triangular matrices have zeros above or below the main diagonal of a square matrix.
- The determinant of a matrix is a scalar value obtained from the products of the matrix's elements according to certain constraints.
- A banded matrix is a sparse matrix with nonzero elements confined to a diagonal band around the main diagonal.
- The transpose of a matrix exchanges the rows and columns of the original matrix.
- The inverse of an invertible square matrix results in the identity matrix when multiplied by the original.Matrices
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This document discusses matrices and their properties. It defines what a matrix is and different types of matrices such as line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also covers operations that can be performed on matrices, including addition, subtraction, scalar multiplication, and matrix multiplication. Properties of these operations are provided.More Related Content
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The history and development of matrix theory is summarized as follows:
1) The term "matrix" was introduced in 1850 by James Joseph Sylvester to describe rectangular arrays of numbers or expressions arranged in rows and columns.
2) The founder of modern matrix theory is considered to be Arthur Cayley, who in the 1850s introduced concepts such as inverse matrices and matrix multiplication.
3) Important developments in matrix theory continued throughout the 19th and 20th centuries, including the discovery by Arthur Cayley and William Hamilton of unique properties of matrices.Matrices
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This document defines and describes various types of matrices. It defines a matrix as a rectangular array of numbers or functions with m rows and n columns referred to as an m x n matrix. It then lists and defines the following types of matrices: row matrix, column matrix, null matrix, rectangular matrix, square matrix, diagonal matrix, scalar matrix, unit matrix, symmetric matrix, and skew-symmetric matrix. It provides examples of each type of matrix and their general syntax.Notes of Matrices and Determinants
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This document covers matrices, determinants, and their properties. Some key points:
- A matrix is a rectangular arrangement of numbers. The order of a mn matrix is defined by its m rows and n columns.
- A square matrix is symmetric if it is equal to its transpose, and skew-symmetric if it is equal to the negative of its transpose.
- The determinant of a square matrix provides a number associated with the matrix, denoted |A| or detA.
- Properties of determinants include that the value does not change under row/column interchange operations, and that multiplying a row/column by a constant k multiplies the determinant by k.MATRICES
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This document defines and describes different types of matrices including:
- Upper and lower triangular matrices
- Determinants which are scalars obtained from products of matrix elements according to constraints
- Band matrices which are sparse matrices with nonzero elements confined to diagonals
- Transpose matrices which exchange the rows and columns of a matrix
- Inverse matrices which when multiplied by the original matrix produce the identity matrixMatrices y determinants
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This document discusses matrices and their properties. It defines a matrix as a rectangular array of numbers arranged in rows and columns. It describes several types of matrices including line matrices, column matrices, square matrices, diagonal matrices, identity matrices, symmetric matrices, triangular matrices, and inverse matrices. It also explains common operations that can be performed on matrices such as addition, subtraction, scalar multiplication, and multiplication. Key properties of these matrix operations are provided.Matrices 1
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This document provides an overview of matrices and basic matrix operations. It discusses what matrices are, how to perform operations like addition, multiplication, and taking the transpose. It also covers special types of matrices like diagonal, triangular, and identity matrices. It explains how to calculate the determinant of a 2x2 matrix and find the inverse of a 2x2 matrix using the determinant. The goal is for the reader to understand matrices, common operations, and how to calculate the determinant and inverse of a 2x2 matrix after reviewing this material.MATRICES
MATRICESfaijmsk
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This document provides an overview of matrices and matrix operations. It begins by stating the objectives of understanding matrix characteristics, applying basic matrix operations, knowing inverse matrices up to 3x3, and solving simultaneous linear equations up to 3 variables. It then defines what a matrix is, discusses matrix dimensions and types of matrices. The document outlines various matrix operations including addition, subtraction, multiplication and scalar multiplication. It provides examples of how to perform these operations. It also covers the transpose of a matrix and inverse matrices.INTRODUCTION TO MATRICES, TYPES OF MATRICES,
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油
Matrices can be added, subtracted, and multiplied under certain conditions.
Addition and subtraction require matrices to be the same size.
Matrix multiplication requires the number of columns of the first matrix to equal the number of rows of the second matrix.
Matrices can also be multiplied by scalars.Matrix.
Matrix.Awais Bakshy
油
The document defines and provides examples of different types of matrices, including:
- Square matrices, where the number of rows equals the number of columns.
- Rectangular matrices, where the number of rows does not equal the number of columns.
- Row matrices, with only one row.
- Column matrices, with only one column.
- Null or zero matrices, with all elements equal to zero.
- Diagonal matrices, with all elements equal to zero except those on the main diagonal.
The document also discusses transpose, adjoint, and addition of matrices.Matrices And Determinants
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Matrices are widely used in business, economics, and other fields. They allow problems to be represented with distinct finite numbers rather than infinite gradations as in calculus. Sociologists, demographers, and economists use matrices to study groups, populations, industries, and social accounting. [/SUMMARY]Introduction of matrix
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The document defines various types of matrices including row vectors, column vectors, submatrices, square matrices, triangular matrices, diagonal matrices, identity matrices, zero matrices, and diagonally dominant matrices. It provides examples of each type of matrix. It also discusses when two matrices are considered equal, which is when they have the same size and corresponding elements are equal.Matrices - multiplication of matrices
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- The document discusses how to multiply matrices, including defining when multiplication is valid based on the number of columns and rows of the matrices.
- It provides an example of multiplying two matrices, showing the step-by-step process of multiplying corresponding elements and summing them.
- It also discusses properties of matrix multiplication, including associativity, distributivity, and the existence of an identity matrix.
- Examples are provided to illustrate verifying these properties by calculating different matrix multiplications.M a t r i k s
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油
1. The document discusses various types and operations of matrices including transpose, similarity, inverse, and determinant of matrices.
2. It also discusses using matrices to solve systems of linear equations by finding the inverse of the coefficient matrix or calculating the determinant.
3. The key matrix concepts covered are matrix notation, types of matrices, matrix addition/subtraction, multiplication, and using matrices to represent and solve linear systems.Matrix and it's application
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The document discusses matrices and their types and applications. It defines a matrix as a rectangular arrangement of numbers, expressions or symbols arranged in rows and columns. It describes 10 different types of matrices including row, column, square, null, identity, diagonal, scalar, transpose, symmetric and equal matrices. It also discusses three algebraic operations on matrices: addition, subtraction and multiplication. Finally, it provides examples of how matrices are used in economics to calculate costs of production, in geology for seismic surveys, and in robotics and automation to program robot movements.Algebraic Properties of Matrix Operations
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The m x n matrix with all entries of zero is denoted by _ , for a matrix A of size m x n, we have:
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This document is an introduction to matrices presented by Reza At-Tanzil of the Department of Pharmacy at Comilla University. It defines what a matrix is, describes different types of matrices including column/row matrices, rectangular matrices, square matrices, diagonal matrices, identity matrices, null matrices, and scalar matrices. It also covers matrix operations such as matrix multiplication, transpose of a matrix, symmetric matrices, inverse of a matrix, and adjoint matrices.Determinants
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The document discusses determinants and their properties. It defines determinants as representing single numbers obtained by multiplying and adding matrix elements in a special way. It then provides formulas for calculating determinants of matrices of order 1, 2 and 3. It also outlines several properties of determinants, such as how interchanging rows/columns, multiplying rows by constants, and adding rows affects the determinant. Finally, it discusses how determinants are used to determine whether systems of linear equations are consistent or inconsistent.Lesson 1 - Introduction to Matrices
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The document defines key terms and concepts relating to matrices. It explains that a matrix is a two-dimensional array with rows and columns used to organize data. Matrices allow for simple display of data with non-essential information removed. They have various applications including graphic design and solving equations. The document defines order, elements, and notation for referring to entries in a matrix. It provides examples for stating the order, values, and positions of elements in matrices. Finally, it describes special types of matrices such as column, row, square, and triangular matrices as well as properties like the transpose and leading diagonal.Similar to Matrices (20)
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This document defines and explains different types of matrices:
- Upper and lower triangular matrices have zeros above or below the main diagonal of a square matrix.
- The determinant of a matrix is a scalar value obtained from the products of the matrix's elements according to certain constraints.
- A banded matrix is a sparse matrix with nonzero elements confined to a diagonal band around the main diagonal.
- The transpose of a matrix exchanges the rows and columns of the original matrix.
- For matrix multiplication to be defined, the number of columns of the left matrix must equal the number of rows of the right matrix.Basic concepts. Systems of equations
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This document defines and provides examples of different types of matrices:
- Upper and lower triangular matrices have zeros above or below the main diagonal of a square matrix.
- The determinant of a matrix is a scalar value obtained from the products of the matrix's elements according to certain constraints.
- A banded matrix is a sparse matrix with nonzero elements confined to a diagonal band around the main diagonal.
- The transpose of a matrix exchanges the rows and columns of the original matrix.
- The inverse of an invertible square matrix results in the identity matrix when multiplied by the original.Matrices
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Matrices and their operations were discussed. Key points include:
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A matrix is a rectangular array of numbers arranged in rows and columns. There are several types of matrices including square, rectangular, diagonal, identity, and triangular matrices. Operations that can be performed on matrices include addition, subtraction, multiplication by a scalar, and determining the transpose, determinant, and inverse of a matrix. A C program is shown that uses nested for loops to input and output the elements of a matrix.ALLIED MATHEMATICS -I UNIT III MATRICES.ppt
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The document defines and explains matrices and various operations that can be performed on matrices. It defines a matrix as a rectangular array of real numbers arranged in rows and columns. It describes types of matrices such as square, diagonal, scalar, and identity matrices. It then explains different operations that can be done on matrices, including addition, scalar multiplication, dot product, matrix multiplication, and matrix transposition. It provides examples of evaluating these operations and lists some properties of matrix operations.Matrix and its operations
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Matrices can be added, subtracted, and multiplied according to certain rules.
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The document defines matrices and provides examples of different types of matrices. It discusses key concepts such as rows, columns, dimensions, entries, addition, subtraction, and multiplication of matrices. It also covers special matrices like identity matrices, inverse matrices, transpose of matrices, and using matrices to solve systems of linear equations. The document is a comprehensive overview of matrices that defines fundamental terms and concepts.systems of linear equations & matrices
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This document provides an overview of matrices and matrix operations. It defines what a matrix is and discusses matrix order and elements. It then covers basic matrix operations like scalar multiplication, addition, and multiplication. It introduces the concepts of transpose, special matrices like diagonal and triangular matrices, and the null and identity matrices. The document aims to define fundamental matrix concepts and arithmetic operations.
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introduction to business statistics, various measures of statistics like mean ,mode , mode, dispersion and business mathematics aswell.
Matrices & Determinants.pdf
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1. The document discusses matrices and various matrix operations.
2. It defines what a matrix is and different types of matrices such as row matrix, column matrix, square matrix, diagonal matrix, triangular matrix, and null matrix.
3. It covers matrix addition and multiplication. Matrix addition involves adding corresponding elements of two matrices of the same size. Matrix multiplication is only defined if the number of columns of the first matrix equals the number of rows of the second matrix.More from mariacadena (10)
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This document discusses different methods for solving systems of linear equations, including Cramer's rule, elimination methods, and Gaussian elimination. Cramer's rule uses determinants to find the values of variables by dividing the determinant of the coefficients by the primary determinant. Elimination methods remove one unknown using multiplication and addition of equations. Gaussian elimination transforms the coefficient matrix into row echelon form through elementary row operations to solve the system.System of equations
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This document discusses different methods for solving systems of linear equations, including Cramer's rule, elimination methods, and Gaussian elimination. Cramer's rule uses determinants to find the values of variables by dividing the determinant of the coefficients by the primary determinant. Elimination methods remove one unknown using addition or subtraction of equations. Gaussian elimination transforms the coefficient matrix into row echelon form through elementary row operations to solve the system. The document provides examples of applying each method to solve sample systems of linear equations.System of equations
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This document discusses different methods for solving systems of linear equations, including Cramer's rule, elimination methods, and Gaussian elimination. Cramer's rule uses determinants to find the values of variables by dividing the determinant of the coefficients by the primary determinant. Elimination methods remove one unknown using multiplication and addition of equations. Gaussian elimination transforms the coefficient matrix into triangular form using row operations, then back substitution can find the unique solution.
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Este documento explica c坦mo calcular la inversa de una matriz cuadrada no singular utilizando el m辿todo de Gauss-Jordan. Primero define qu辿 es una matriz inversa y luego describe el m辿todo de Gauss-Jordan para transformar una matriz ampliada compuesta por la matriz original y una matriz identidad en una matriz donde la matriz original es la matriz identidad, obteniendo as鱈 su inversa. Finalmente, compara los m辿todos de inversi坦n de matrices y eliminaci坦n para resolver sistemas de ecuaciones.
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El m辿todo de Gauss-Seidel es una t辿cnica para resolver grandes sistemas de ecuaciones lineales simult叩neas. Funciona iterando los valores de las inc坦gnitas y actualizando uno por uno basado en el coeficiente dominante en cada ecuaci坦n, convergiendo a una soluci坦n cuando los coeficientes cumplen ciertas condiciones. El documento provee los pasos del m辿todo y un ejemplo num辿rico para ilustrar su aplicaci坦n.System of equations
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This document discusses different methods for solving systems of linear equations, including Cramer's rule, elimination methods, and Gaussian elimination. Cramer's rule uses determinants to find the values of variables by dividing the determinant of the coefficients by the primary determinant. Elimination methods remove one unknown using row operations like addition and subtraction. Gaussian elimination transforms the coefficient matrix into triangular form using row operations, then back substitution can find the unique solution.
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El documento resume diferentes m辿todos para encontrar las ra鱈ces de una ecuaci坦n, incluyendo el m辿todo de bisecci坦n, la posici坦n falsa, el punto fijo, Newton-Raphson y el m辿todo de secado. Explica que cada m辿todo toma un intervalo inicial y realiza iteraciones para encontrar la ra鱈z mediante la evaluaci坦n de la funci坦n y posibles derivadas en cada paso.
Roots of equations workedmariacadena
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Este documento describe m辿todos para encontrar las ra鱈ces de ecuaciones, incluyendo bisecci坦n, posici坦n falsa, punto fijo, Newton-Raphson y secado. Explica que el m辿todo de bisecci坦n itera entre dos puntos para encontrar un intervalo que contenga la ra鱈z, mientras que el m辿todo de posici坦n falsa calcula un nuevo punto basado en las funciones de los puntos existentes. Los m辿todos de Newton-Raphson y secado usan derivadas para iterar hacia la ra鱈z, y el m辿todo de punto fijo iguala la funci坦n a la identidad.
Roots of equations workedmariacadena
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El documento resume diferentes m辿todos para encontrar las ra鱈ces de una ecuaci坦n, incluyendo el m辿todo de bisecci坦n, la posici坦n falsa, el punto fijo, Newton-Raphson y el m辿todo de secado. Explica que cada m辿todo toma un intervalo inicial y realiza iteraciones para encontrar la ra鱈z mediante la evaluaci坦n de la funci坦n y posibles derivadas en cada paso.Matrices
- 1. MATRICESMar鱈a Isabel Cadena M辿todos Num辿ricos
- 2. TYPES OF MATRICESUPPER TRIANGULAR MATRIX:The matrix A = (aij) a square matrix of order n. We say that A is upper triangular if all elements of A situated below the main diagonal are zero, ieaij = 0 for all i> j, i, j = 1 ,...., nFor example the matrices
- 3. LOWER TRIANGULAR MATRIX:The matrix A = (aij) a square matrix of order n. We say that A is lower triangular if all elements of A located above the main diagonal are zero, ieaij = 0 for all i <j, i, j = 1 ,...., nFor example, arrays
- 4. MATRIX TRANSPOSE: Given a matrix A, is called the matrix transpose of the matrix A is obtained by changing sort rows by the columns.(At)t = A
- 5. (A + B)t = At + Bt
- 6. (留油揃A)t = 留揃 At
- 7. (A 揃 油B)t = Bt 揃 AtSymmetric matrix A symmetric matrix is a square matrix that verifies:A = At.MATRIX INVERSEThe product of a matrix by its inverse equals the identity matrix.A 揃 A-1 = A-1 属 A = IPROPERTIES(A 属 B) -1 = B-1 to-1(A-1) -1 = A(K A) -1 = k-1 to-1(A t) -1 = (A -1) t
- 8. OPERATIONS WITH MATRICESSUM OF MATRICES:Given two matrices of the same size, A = (aij) and B = (bij) is defined as the matrix sum: A + B = (aij + bij).The matrix sum is obtained by adding the elements of the two arrays that occupy the same same position.
- 9. Properties of matrixaddition:Internal:The sum of two matrices of order mxn matrix is another dimension mxn.
- 10. Associations:A + (B + C) = (A + B) + C
- 11. Neutral element:A + 0 = AWhere O is the zero matrix of the same dimension as matrix A.
- 12. Opposite element:A + (-A) = OThe matrix is opposite that in which all elements are changed in sign.
- 13. Commutative:A + B = B + AProduct of a scalar by a matrix:Given a matrix A = (aij) and a real number kR, defines the product of a real number by a matrix: the matrix of the same order as A, in which each element is multiplied by k.kA=(k aij)
- 14. Product Matrix:Two matrices A and B are multiplied if the number of columns of A matches the number of rows of B.Mm Mn x x n x m x p = M pThe element cij of the matrix product is obtained by multiplying each element in row i of matrix A for each element of column j of the matrix B and adding.油
- 15. Product features matrix:Associations:A 属 (B 属 C) = (A 属 B) 属 C
- 16. Neutral element:A 揃 I = AWhere I is the identity matrix of the same order as the matrix A.
- 17. Not Commutative:A 揃 B B * A
- 18. Product distributive over addition:A 属 (B + C) = A 属 B + A C.BIBLIOGRAPHYhttp://www.ditutor.comwww.fisicanet.com