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Introduction
 Matrices and vectors (Linear Algebra) are the basic elements in
MATLAB and also the basic elements in control design theory
- So, it is important you know how to handle vectors and
matrices in MATLAB
 General matrix 𝐴 may be written,
A=

VECTORS
 The vector is created by typing the elements (numbers) inside
square brackets [ ]
 To separate rows, we use a semicolon “;”
 To separate columns, we use a comma “,” or a space “ ”
Example: Create the following vector in command window
variable_name = [ type vector elements ]
1. A =

Keep in Mind !!
 An array of dimension is called a row vector
 An array of dimension is called a column vector
 A row vector is converted to a column vector using the
transpose operator denoted by apostrophe or a single quote
(')

Creating a vector with constant spacing
x = []
Starting Value Final Value
Increment
Example:
Create a vector with element with increment
of

Creating a vector with linear (equal) spacing
 A vector with n elements that are linearly (equally) spaced in
which the first element is and the last element is can be created
by typing the linspace command (MATLAB determines the
correct spacing)
 First element


Note: When the number of elements is omitted, the default is 100
variable_name = linspace(

ACCESS BLOCKS OF ELEMENTS
- To access blocks of elements, we use MATLAB's colon
notation (:)
Example:
1. v (1:3) : Access the first three elements of v
2. v(3:end) : Access all elements from the third through the last
element (end signifies the last element in the vector)
3. v(:) : Produces a column vector
4. v(1:end) : Produces a row vector

MATRICES
 A matrix is an array of numbers. To type a matrix into MATLAB
you must;
1. begin with a square bracket, [
2. separate elements in a row with spaces or commas (,)
3. use a semicolon (;) to separate rows
4. end the matrix with another square bracket, ]

Cont.. .
Dimension
 To determine the dimensions of a matrix or vector, use the
command size
Continuation
 If it is not possible to type the entire row input on the same
line, use consecutive periods, called an ellipsis … , to
signal continuation, then continue the input on the next line
[m,n] = size(A)

Transposing a matrix
 The transpose operation is denoted by an apostrophe or a single
quote (‘)
 It flips a matrix about its main diagonal and it turns a row vector
into a column vector

Matrix generators
 MATLAB provides functions that generates elementary matrices
as shown in the table below
eye(m,n) Returns an m-by-n matrix with 1 on the main diagonal
eye(n) Returns an n-by-n square identity matrix
zeros(m,n) Returns an m-by-n matrix of zeros
ones(m,n) Returns an m-by-n matrix of ones
diag(A) Extracts the diagonal of matrix A
rand(m,n) Returns an m-by-n matrix of random numbers

Cont.. .
Note: For a complete list of elementary matrices and
matrix manipulations, type help elmat or doc elmat
triu(A) returns the upper triangular portion of matrix A
tril(A) returns the lower triangular portion of matrix A

ARRAY OPERATIONS
o MATLAB has two different types of arithmetic operations:
 matrix arithmetic operations
 array arithmetic operations

MATRIX ARITHMETIC OPERATIONS
: is valid if A and B are of the same size
: multiplies each element of α
: is valid if A is square and equals A*A
: is valid if A's number of column equals B's
number of rows

ARRAY ARITHMETIC OPERATIONS
o Array arithmetic operations or array operations for short, are
done element-by-element
o The period character, ., distinguishes the array operations from
the matrix operations
o Matrix and array operations are the same for addition (+) and
subtraction (-), the character pairs (.+) and (.-) are not used

Cont.. .
Example:
Find from
A = B =

MATRIX FUNCTIONS
o MATLAB provides many matrix functions for various
matrix/vector manipulations

SOLVING LINEAR EQUATIONS
o One of the problems encountered most frequently in scientific
computation is the solution of systems of simultaneous linear
equations
o With matrix notation, a system of simultaneous linear equations
is written
Where,
 : is a given square matrix of order n
 : is a given column vector of n components,
 : is an unknown column vector of n components
𝑨𝒙 =𝒃

Example
Consider the following system of linear equations,
The coefficient matrix A is
A = B =

Cont.. .
This equation can be solved for x using linear algebra. The result is
There are typically two ways to solve for x in MATLAB
1. The first one is to use the matrix inverse, inv
𝒙= 𝑨−𝟏
𝒃

Cont.. .
1. The second one is to use the backslash ( ) operator

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5_Vectors & Matrices for Engineers .pptx

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