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Finding Jordan canonical form?

Apr 05, 2011 by Zorroman | Posted in Mathematics

I'm trying to find all possible Jordan forms for a real matrix whose characteristic and minimal polynomials are as follows: characteristic is f(x) = (x-1)^4 * (x-2)^2, and minimal is m(x) = (x-1)^2 * (x-2)^2.

I'm also trying to prove that

The minimal polynomial tells us that the biggest Jordan Blocks for the eigenvalues 1 and 2
are both 2 x 2 blocks and that we need at least one of each.

For x = 2, this is it, since the minimal and characteristic polynomial has the

Example of Jordan Canonical Form: 2x2 Matrix

Matrix Theory: Find the Jordan form for the real 2 x 2 matrix A = [0 -4 \ 1 4]. For this matrix, there is no basis of eigenvectors, so it is not ...