Week - 1 |
Vector Spaces, operations with vectors |
Week - 2 |
Vector Spaces, lines and planes , |
Week - 3 |
Euclidean Spaces, Linearly dependent and independent vectors. |
Week - 4 |
Dimension and basis concepts for vector spaces; Subspaces. |
Week - 5 |
Matrices and matrix operations |
Week - 6 |
Determinant and its properties |
Week - 7 |
The matrix inverse |
Week - 8 |
Linear transformations and properties |
Week - 9 |
Rank and determinants |
Week - 10 |
Elementary transformations, echelon matrices and rank. |
Week - 11 |
Systems of linear equation |
Week - 12 |
Systems of homogeneous linear equations; Solution subspaces; |
Week - 13 |
Eigenvalue and Eigenvectors; |
Week - 14 |
Quadratic forms, positive definiteness. |