### MA5310 Linear Algebra

#### Course Details

Unit 1. Vector spaces, subspaces, basis and dimension, coordinates, algebra of linear transformations, isomorphisms, representation of linear transformations by matrices, linear functionals and annihilators, double dual and transpose of a linear transformation. (14 lectures)

Unit 2. Characteristic values and characteristic polynomials, diagonalizabletransformations, annihilating polynomials, Cayley-Hamilton theorem, invariant subspaces and triangular form, simultaneous triangularization and diagonalization, direct sum decompositions, invariant direct sums, primary decompostion theorem. (14 lectures)

Unit 3. Inner product spaces, adjoints, unitary and normal transformations, spectral Theorem, Jordan canonical form. (12 lectures)

#### Course References:

Text Books:

1. K. Hoffman and R. Kunze: Linear Algebra, 2nd Edition, Prentice Hall of India, 2005

2. S. Axler: Linear Algebra Done Right, 2nd Edition, Springer UTM, 1997.

Reference Books:

1. P. Halmos, Finite dimensional vectors paces, Springer, 1974.

2. Peter D. Lax, Linear algebra, Wiley student edition, 1997.

3. E.B. Vinberg, A course in algebra, Graduate text in Mathematics, volume 56, AMS, 2003.

4. M. Thamban Nair and Arindama singh, Linear algebra, Springer, 2018.