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

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.

4. Graph Theory

5. Network Models
• Determine the currents I1, I2, and I3 for the following
electrical network:

6. By Kirchhoff’s Law

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.

13. Thank you