podprzestrzeniom
Podprzestrzeniom is the dative plural form of podprzestrzeń, the Polish term for subspaces. In mathematics, a subspace of a vector space V over a field F is a subset W that is itself a vector space under the same operations as V.
To qualify as a subspace, W must satisfy three conditions: it contains the zero vector, is closed
In R^3 with the standard operations, lines through the origin and planes through the origin are subspaces;
Given a subset S of V, the subspace spanned by S consists of all finite linear combinations
The intersection of subspaces is a subspace; the sum U+W is the set of all u+w with
Subspaces underpin many linear algebra techniques, including projections, decompositions, and the study of linear systems, eigenvectors,