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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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