# Find the Jordan form of this Matrix

M y question is relating to the matrix as A. I have started off this problem by finding the eigenvalues, which turns out to be 3 ( I should note that it has an algebraic multiplicty of 3)

From there I have found the corresponding Eigenspace which is $E_3=span(-1,1,1)$

I am little confused as to what to do from here.

• If the eigenspace was 3D, then you could construct an orthonormal basis consisting of eigenvectors and you'd get a diagonal matrix, or a matrix with 3 $1 \times 1$ Jordan blocks on the diagonal. As the geometric multiplicity becomes less than the algebraic multiplicity, the size of the Jordan block increases because you can't construct an orthogonal basis of eigenvectors for the eigenspace. Hope this clarified a bit. – Merkh Jun 20 '16 at 13:07