Syllabus
Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations. Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Matrix representation of linear transformations. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms. Inner product spaces, orthonormal basis. Quadratic forms, reduction and classification of quadratic forms
Course Curriculum
| INTRODUCTION | |||
| Introduction to Matrices | 02:17:00 | ||
| Rank of Matrix | 00:54:00 | ||
| Linear Equations | 02:04:00 | ||
| Determinant | 02:14:00 | ||
| VECTOR SPACE AND LINEAR EQUATIONS | |||
| Revision of Matrices | 02:03:00 | ||
| Vector Spaces | 01:05:00 | ||
| Linear Equations – Vector Space Approach | 01:43:00 | ||
| Basis and Dimensions | 02:35:00 | ||
| Change of Basis | 01:34:00 | ||
| INNER PRODUCT SPACES | |||
| Orthogonality | 01:52:00 | ||
| Inner Product Spaces | 01:08:00 | ||
| EIGENVALUES AND EIGENVECTORS | |||
| Introduction to Eigenvalues and Eigenvectors | 00:36:00 | ||
| Diagonalisation of Matrices and its Applications | 00:59:00 | ||
| Properties of Eigenvalues | 00:18:00 | ||
| Symmetric Matrices | 01:09:00 | ||
| Cayley Hamilton Equation | 00:08:00 | ||
| Similar Matrices | 00:16:00 | ||
| LINEAR TRANSFORMATION | |||
| Introduction to Linear Transformation | 01:02:00 | ||
| Matrix of Linear Transformation | 00:50:00 | ||
| JORDAN FORM | |||
| Jordan Form | 01:45:00 | ||
| Generalised Eigenvectors | 01:01:00 | ||
| QUADRATIC FORM | |||
| Quadratic Form | 01:52:00 | ||
| BILINEAR FORM | |||
| Bilinear Form | 01:07:00 | ||
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