Is there an easy way to check when geometric multiplicity is equivalent to the algebraic multiplicity?

Question

Suppose I have a matrix $A$, not telling you what it looks like, and the set of eigenvalues associated with $A$ = $\{-1,-1,-1,4\}$

Suppose the geometric multiplicity of $-1$ is $2$, what would be the geometric multiplicity of $4$?

Possible answer could be $1$, $2$, since any more then our jordan form will blow up

Obviously here the algebraic multiplicity of $4$ is one.

Does it equal to the geometric multiplicity?

What is a condition to check when they are equal and how can I see that?

Answer 1

Algebraic multiplicity $\geq$ geometric multiplicity. Geometric multiplicity never exceeds algebraic multiplicity, hence $4$ has the geometric multiplicity $1$