nLab matrix algebra

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.

Related concept

• square matrix