#
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 square 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 $n \times n$-matrices is equivalently the groupoid convolution algebra of the pair groupoid on the set with $n$-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 December 1, 2019 at 04:34:37.
See the history of this page for a list of all contributions to it.