MA6005 Applied Linear Algebra
Inner Product Spaces: Normal, Unitary and Self-adjoint operators, Finite Dimensional Spectral theorem for normal operators. Quadratic forms, difference equations. Orthogonal reduction, Discrete Fourier Transform, complementary subspaces, range-null space decomposition, orthogonal decomposition, singular-value decomposition, orthogonal projection, least squares solutions. Perron Frobenius Theory: Positive matrices, Nonnegative matrices, Stochastic matrices and applications to Markov chains.
1. K. Hoffman and R. Kunze, Linear Algebra, Prentice-Hall, Second Edition,2008.
2. C. D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2001.