nLab
matrix algebra

Contents

Context

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Idea

The associative algebra of matrices over some ring under matrix multiplication is the coresponding matrix algebra.

Properties

General

The multiplicative identity element in a matrix algebra is the identity matrix.

Relation to groupoid algebras

The algebra of n×nn \times n-matrices is equivalently the groupoid convolution algebra of the pair groupoid on the set with nn-elements.

Norms

The matrix algebra over a normed ring is naturally itself a normed ring. See at normed ring – Examples – matrix ring.

Last revised on November 9, 2019 at 06:08:23. See the history of this page for a list of all contributions to it.