### MA 219: Linear Algebra

#### Credits: 3:0

Vector spaces: Definition, Basis and dimension, Direct sums. Linear transformations: Definition, Rank-nullity theorem, Algebra of linear transformations, Dual spaces, Matrices.

Systems of linear equations:elementary theory of determinants, Cramer’s rule. Eigenvalues and eigenvectors, the characteristic polynomial, the Cayley- Hamilton Theorem, the minimal polynomial, algebraic and geometric multiplicities, Diagonalization, The Jordan canonical form. Symmetry: Group of motions of the plane, Discrete groups of motion, Finite groups of S0(3). Bilinear forms: Symmetric, skew symmetric and Hermitian forms, Sylvester’s law of inertia, Spectral theorem for the Hermitian and normal operators on finite dimensional vector spaces.

#### Suggested books :

1. Artin, M., Algebra ,Prentice_Hall of India, 1994.
2. Halmos, P., Finite dimensional vector spaces ,Springer-Verlag (UTM), 1987.
3. Hoffman, K. and Kunze, R., Linear Algebra (2nd Ed.) ,Prentice-Hall of India, 1992.

#### All Courses

Contact: +91 (80) 2293 2711, +91 (80) 2293 2625
E-mail: chairman.math[at]iisc[dot]ac[dot]in