# Finding the Jordan Canonical form using known Ranks for a generalized eigenvector to certain powers.

Can someone please expand on this idea from wikipedia https://en.wikipedia.org/wiki/Jordan_normal_form, under Generalized Eigenvector - Uniqueness.

Particularly, how you can use the rank of $$(A - \lambda I)^{k_1-2}$$ to find the the number of Jordan Blocks for $$k_1-1$$. But then it says the general case is similar, but I do not quite understand what the next step given further ranks. My question is how would you use the rank of $$(A - \lambda I)^{k_1-3}$$ to determine the number of Jordan blocks for $$k_1-2$$ and so on?

• Think about what happens to the nullity of successive power of $A-\lambda I$ in terms of the Jordan chains for each independent eigenvector. – amd Apr 21 at 20:09