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)
Test-1 -15 marks (one hour test) after 15th lecture.
CA - 20 marks (Quizzes / assignments / lab practice) Test – 2- 15 marks (two-hour test) at the end of 30th lecture.
End semester- 50 marks (three hour test) at the end of the course. Total - 100 marks.
Supplementary exam for this course will be conducted as a three-hour test for 50 marks.