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Matrix Analysis/

(earlier MAI0098)

Number of credits: 8 hp

Examiner: Göran Bergqvist

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

Course 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.

Organisation: Lectures.

Examination: Hand-in assigments and oral presentations.

Prerequisites: 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).

Course homepage

Page manager: karin.johansson@liu.se
Last updated: 2023-02-27