Let 
be a matrix with the elementary divisors of its characteristic matrix expressed as
powers of its irreducible polynomials in the field ![F[lambda]](/images/equations/JacobsonCanonicalForm/Inline2.svg)
, and consider an elementary divisor ![[p(lambda)]^q](/images/equations/JacobsonCanonicalForm/Inline3.svg)
. If 
, then
![C_q(p)=[C(p) M 0 ... 0 0; 0 C(p) M ... 0 0; | ... ... ... ... |; 0 0 0 ... C(p) M; 0 0 0 ... 0 C(p)],](/images/equations/JacobsonCanonicalForm/NumberedEquation1.svg) |
where 
is a matrix of the same order as 
having the element 1 in the lower left-hand corner and
zeros everywhere else.
