Matrix Analysis, 8.0 credits

Entry requirements

Linear Algebra, honours course (TATA53) or equivalent (the following topics should be familiar: complex vector spaces, the spectral theorem for Hermitian and normal operators, the singular value decomposition, the Jordan normal form).

Contents

• Special matrices: Toeplitz, circulant, Vandermonde, Hankel, and Hessenberg matrices.
• Block matrices: inversion formulas, Schur complement.
• Real and complex canonical forms.
• Vector and matrix norms.
• Eigenvalues: location, inequalities, perturbations, Rayleigh quotients, variational characterization. Hadamard´s inequality.
• Singular values: inequalities, variational characterization, Schatten and Ky Fan norms.
• Total least squares. Quadratic minimization with linear constraints.
• Matrix products: Kronecker, Hadamard and Khatri-Rao products.
• Matrix equations. Stable matrices.
• Functions of matrices.
• Matrices of functions, matrix calculus and differentiation.
• Multilinear algebra, tensor product, decomposition and approximation of tensors.

Educational methods

Lectures.

Examination

Hand-in assigments and oral presentations.

Grading

Course literature

Horn and Johnson: Matrix Analysis (recommended), lecture notes.