Jodan Normal Form if geometric mult. < alg. mult

Let's say we have a matrix $A\in M_{n,n}(\mathbb R)$.

Assume tht for the eigenvalue $\lambda_1$ we have:

Algebraic Multiplicty: 4

Geometric Multiplicity: 2

Is then the correspodning jordan block alwas the sum of two blocks of size 2 or is it also possible that we have one block of size 1 and one block of size 3?

• You just said it. It is indeed possible. – user228113 Feb 4 '17 at 13:54
• In general, what completely determines the JNF of a matrix with just one eigenvalue $\lambda$ is the sequence $\dim\ker(A-\lambda I)^k$ for $k=1,2,\cdots,n-1$. – user228113 Feb 4 '17 at 13:58