Advanced Linear Algebra

Code: MA424 | L-T-P-C: 3-0-0-6

Review of vector spaces, bases and dimensions, direct sums; Linear transformations, ranknullity theorem, matrix representation of linear transformations, trace and determinant; Eigenvalues and eigenvectors, invariant subspaces, upper triangular matrices, invariant subspaces on real vector spaces, generalized eigenvectors, characteristic and minimal polynomials, triangulation, diagonalization, Jordan canonical form; Norms and innerproducts, orthonormal bases, orthogonal projections, linear functional and adjoints, selfadjoint and normal operators, Schur decomposition, spectral theorems for selfadjoint, unitary and normal operators, positive definite operators, isometry, polar and singular value decompositions.

Texts:

1. S. Axler, Linear Algebra Done Right, 2nd edition, Springer-Verlag, 1997.
2. K. Hoffman and R. Kunze, Linear Algebra, Pearson Education India, 2003.