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6FMAI14
Matrix Analysis/
Matrisanalys
(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).
Sidansvarig:
karin.johansson@liu.se
Senast uppdaterad: 2023-02-27