Jacobson Canonical Form

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.