Göm menyn

Polopoly kommer stängas 15 december 2023. Innan dess behöver kvarvarande sidor flyttas eller kommer tas bort. Medarbetare kan läsa mer på FAQ Polopoly Avveckling

Den efterfrågade sidan finns ej på det önskade språket.

Till nästa tillgängliga sida.

Den efterfrågade artikeln finns för dessa språk..

Page in English.

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

Sidansvarig: karin.johansson@liu.se
Senast uppdaterad: 2023-02-27