Similar matrix - Wikipedia, the free encyclopedia Jordan normal form - Wikipedia, the free encyclopedia
Matrices A and B are similar iff their Jordan normal forms are equal (this is because every matrix in an algebraically closed field has a unique Jordan form).

If you know the minimal polynomial of a matrix, then it's easier to calculate its jordan form:

Let

be an algebraically-closed field,

a vector space over

,

represent a linear operator

be the minimal polynomial of A, where each

is the geometrical multiplicity of

, and let

Then by the primary decomposition theorem,

and after a few more steps, we get that each

is represented by a Jordan block matrix:

And the Jordan canonical form of A is the direct sum of its Jordan blocks.