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Applications of Linear Algebra in Computer Sciences

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Amir Sharif Chishti
Amir Sharif Chishti

I introduces some of the applications of linear algebra in Computer Sciences ie: Cryptography, Graph Theory, Networks and Computer Graphics.

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APPLICATIONS OF LINEAR ALGEBRA IN COMPUTER SCIENCES Hafiz Muhammad Amir Sharif SP12-BSCS-B7(B)-110
Objectives ?Importance of Linear Algebra ?Graph Theory ?Network Models ?Cryptography ?Computer Graphics
Why Linear Algebra is important ? ? Linear algebra is vital in multiple areas of science in general. Because linear equations are so easy to solve, practically every area of modern science. ? It converts large number of problems to matrix and thus we solve the matrix.
Graph Theory
Network Models ? Determine the currents I1, I2, and I3 for the following electrical network:
By Kirchhoff¡¯s Law
Cryptography ? Encryption and decryption require the use of some secret information, usually referred to as a key. ? Example Let the message be ¡°PREPARE TO NEGOTIATE¡± ? We assign a number for each letter of the alphabet.
Thus the message becomes: ? Since we are using a 3 by 3 matrix, we break the enumerated message above into a sequence of 3 by 1 vectors:
By multiplying encoding matrix to this matrix we will encrypt the msg
Now to decrypt the msg we have to multiply this matrix to Inverse of encoding matrix ? The inverse of this encoding matrix, the decoding matrix, is: ? Multiplying again by this matrix we will get our Msg.
Computer Graphics ? In computer graphics every element is represented by a MATRIX.
Conclusion: ? There are so many application of Linear Algebra in Computer Science. ? From simple circuit solving to large web engine algorithms.
Thank you

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Applications of Linear Algebra in Computer Sciences

  • 1. APPLICATIONS OF LINEAR ALGEBRA IN COMPUTER SCIENCES Hafiz Muhammad Amir Sharif SP12-BSCS-B7(B)-110
  • 2. Objectives ?Importance of Linear Algebra ?Graph Theory ?Network Models ?Cryptography ?Computer Graphics
  • 3. Why Linear Algebra is important ? ? Linear algebra is vital in multiple areas of science in general. Because linear equations are so easy to solve, practically every area of modern science. ? It converts large number of problems to matrix and thus we solve the matrix.
  • 5. Network Models ? Determine the currents I1, I2, and I3 for the following electrical network:
  • 7. Cryptography ? Encryption and decryption require the use of some secret information, usually referred to as a key. ? Example Let the message be ¡°PREPARE TO NEGOTIATE¡± ? We assign a number for each letter of the alphabet.
  • 8. Thus the message becomes: ? Since we are using a 3 by 3 matrix, we break the enumerated message above into a sequence of 3 by 1 vectors:
  • 9. By multiplying encoding matrix to this matrix we will encrypt the msg
  • 10. Now to decrypt the msg we have to multiply this matrix to Inverse of encoding matrix ? The inverse of this encoding matrix, the decoding matrix, is: ? Multiplying again by this matrix we will get our Msg.
  • 11. Computer Graphics ? In computer graphics every element is represented by a MATRIX.
  • 12. Conclusion: ? There are so many application of Linear Algebra in Computer Science. ? From simple circuit solving to large web engine algorithms.