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Indian Institute of Science Education and Research Berhampur

Mathematics

MTH 102: Linear Algebra (3)

Learning Objectives:

This is the second core course in calculus designed for second year BS-MS students. The course deals with the multivariable calculus of vectors in dimension 2 and higher. The course concludes with an introduction to first order ODEs, and their solutions.

Course Contents:

Review of complex numbers

Matrices, matrix operations, special matrices (diagonal, triangular, symmetric, skew-symmetric, orthogonal, hermitian, skew hermitian, unitary, normal), vectors in Rn and Cn, matrix equation Ax = b, row-reduced echelon form, row space, column space, and rank of a matrix. Determinants. Systems of linear equations

Vector space Rn, linear independence and dependence, linear span, linear subspaces, bases and dimensions

Vector spaces, bases and dimensions, linear transformations, matrix of a linear transformation, rank-nullity theorem

Inner product spaces, orthonormal bases, Gram-Schmidt orthogonalization, projections

Eigenvalues and eigenvectors of a linear operator, characteristic polynomial, diagonalizability of a linear operator, eigenvalues of the special matrices stated above, spectral theorem for real symmetric matrices and its application to quadratic forms, positive definite matrices

Suggested Books:


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