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, hence whose entries are concentrated on the diagonal, is called a diagonal matrix.

The diagonal matrices form a non-central commutative subalgebra of the matrix algebra $Mat_{n \times n}(R)$, isomorphic to the $n$fold direct sum of the ground ring $R$.

Examples

A diagonal matrix with value 1 in all diagonal entries is an identity matrix.

Related concepts

• permutation matrix

• invertible matrix

• Smith normal form

References

See also

• Wikipedia, Diagonal matrices

• Wikipedia, Diagonalizable matrix