Maria Adam

     

 

Matrix Analysis, [5ΕΠ11 - Fifth Semester]

Syllabus

• Block matrix algebra. Determinants and properties of the block matrices. Matrices and linear systems. Rank of matrices. Kronecker product.
• Normal matrices. Hermitian matrices.
• Vector norms. Matrix norms. Relations between norms. Bounds of the eigenvalues of a matrix. Gershgorin circle Theorem. Condition number. Matrix stability of linear systems.
• Characteristic and minimal polynomial of a matrix. Schur decomposition (Schur triangulation). Diagonalization of a matrix. Spectral theorem. Jordan form. LU decomposition. QR decomposition. Singular Value Decomposition (SVD). Polar decomposition. Applications of the decompositions.

[back]