Review of matrices and linear systems of equations. (2 hrs)

Vector Spaces : Vector spaces – Sub spaces – Linear independence – Basis – Dimension – Inner products – Orthogonality – Orthogonal basis – Gram Schmidt Process – Change of basis. (12 hrs)

Orthogonal complements – Projection on subspace – Least Square Principle. (6 hrs)

Linear Transformations : Positive definite matrices – Matrix norm and condition number – QR- Decomposition – Linear transformation – Relation between matrices and linear transformations – Kernel and range of a linear transformation. (10 hrs)

Change of basis – Nilpotent transformations – Similarity of linear transformations – Diagonalisation and its applications –

Jordan form and rational canonical form. (10 hrs)

SVD

Evaluation Pattern

1. Howard Anton and Chris Rorrs, “Elementary Linear Algebra”, Ninth Edition, John Wiley & Sons, 2000. Reference Book:
2. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.
3. Gilbert Strang, “Linear Algebraand its Applications”, Third Edition, Harcourt College Publishers, 1988.

Course Outcomes

CO-PO Mapping