A square matrix whose values for are all zero is called a diagonal matrix.
Examples
A diagonal matrix with value 1 on the diagonal is an identity matrix.
Properties
Schur lemma
Diagonal matrices always commute with all other square matrices of the same size (with respect to matrix multiplication). However, if is an algebraically closed field, then the converse is also true (Schur lemma): the subset of all diagonal matrices is precisely the center of the ring of matrices .