Question

All the eigen values are zero then it is nilpotent

Answer 1

Step-by-step explanation:

Recall that a square matrix is nilpotent is some positive power of it is the zero matrix. (1) (a) Suppose that A ∈ Fn×n has a nonzero eigenvalue λ. ... (b) By (a), a nilpotent matrix can have no nonzero eigenvalues, i.e., all its eigenvalues are 0. (c) Suppose A has all eigenvalues equal to 0.