Algebra (in English) 121001-D
Wykład (WYK) Semestr zimowy 2024/25

Sets, relations, groups, fields, complex numbers.

Vector spaces and subspaces.

Basis, dimension, coordinate systems.

Linear mapping and a matrix of a linear mapping in a coordinate system.

Kernel and rank of a mapping. Determinant. Characteristic polynomials.

Invariant subspaces, eigenvalues and eigenvectors.

Bilinear forms, quadratic forms,

Inner product, norm, unitary space.

Linear isometry and orthogonal matrices. Gram-Schmidt procedure.

Orthogonal projection, properties. Geometric interpretation of least squares procedure.

Convex sets, convex functions, Jensen's inequality.

Multi-facet convex sets. Vertices.

Cones and convex cones.

Multi-facet convex cones. Dual cones and Farkas' lemma.