MTL502
| MTL502 | |
|---|---|
| Linear Algebra | |
| Credits | 4 |
| Structure | 3-1-0 |
| Pre-requisites | |
| Overlaps | |
MTL502 : Linear Algebra
[edit]Revision of existence-uniqueness of solutions of a system of linear equations, elementary row operations, row-reduced echelon matrices. Vector spaces, span of a subset, bases and dimension, quotient spaces, direct sums. Linear transformations, rank-nullity, matrix representation of a linear transformation, algebra of linear transformations, dual space, transpose of a linear transformation. Eigenvalues, eigenvectors, annihilating polynomials, Cayley-Hamilton theorem, invariant subspaces, triangulable and diagonalizable linear operators. Simultaneous triangulation and diagonalization, Primary decomposition theorem, Jordan decomposition. Courses of Study 2024-2025 Mathematics 269Inner product spaces over R (real numbers) and C (complex numbers), Gram-Schmidt orthogonalization process, orthogonal projection, best approximation. Adjoint of a linear operator, unitary and normal operators, spectral theory of normal operators. Bilinear forms, symmetric and skew-symmetric bilinear forms.