Let be a matrix with the elementary divisors of its characteristic matrix expressed as powers of its irreducible polynomials in the field , and consider an elementary divisor . If , then

where is a matrix of the same order as having the element 1 in the lower left-hand corner and zeros everywhere else.

Ayres, F. Jr. *Schaum's Outline of Theory and Problems of Matrices.* New York: Schaum, pp. 205-206,
1962.