nLab diagonal matrix

Idea

A square matrix $(A_{x,y})\in Mat_{n \times n}(R)$ whose values for $x\neq y$ are all zero is called a diagonal matrix.

Examples

A diagonal matrix with value 1 on the diagonal is an identity matrix.

Properties

Diagonal matrices form the center of the ring of matrices under matrix multiplication.

Related concepts

• permutation matrix

• invertible matrix

• Smith normal form

References

See also

• Wikipedia, Diagonal matrices

• Wikipedia, Diagonalizable matrix