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# Applications of Linear Algebra in Computer Sciences

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

1. 1. APPLICATIONS OF LINEAR ALGEBRA IN COMPUTER SCIENCES Hafiz Muhammad Amir Sharif SP12-BSCS-B7(B)-110
2. 2. Objectives Importance of Linear Algebra Graph Theory Network Models Cryptography Computer Graphics
3. 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.
4. 4. Graph Theory
5. 5. Network Models • Determine the currents I1, I2, and I3 for the following electrical network:
6. 6. By Kirchhoff’s Law
7. 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. 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. 9. By multiplying encoding matrix to this matrix we will encrypt the msg
10. 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. 11. Computer Graphics • In computer graphics every element is represented by a MATRIX.
12. 12. Conclusion: • There are so many application of Linear Algebra in Computer Science. • From simple circuit solving to large web engine algorithms.
13. 13. Thank you

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

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