Vector spaces, Bases and dimension, Direct ums, linear transformations, Matrix
algebra, Eigenvalues and eigenvectors, Cayley Hamilton Theorem, Jordan
canonical form., Orthogonal matrices and rotations, Polar decomposition.,
Bilinear forms.
Suggested books and references:
Artin, M., Algebra, Prentice-Hall of India, 1994.
Hoffman, K and Kunze R., Linear Algebra, Prentice-Hall of India, 1972.
Halmos, P.R., Finite dimensional vector spaces, van Nostrand, 1974 .
Greub, W.H., Linear algebra, Springer-Verlag, 1967.