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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 equat...
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.
• Exam...
Thus the message becomes:

• Since we are using a 3 by 3 matrix, we break the enumerated

message above into a sequence of...
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...
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...
Thank you
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Applications of Linear Algebra in Computer Sciences

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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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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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