Kunze Linear Algebra · Problem 6.3.3

Elementary Canonical Forms

Mathematics — Methods · characteristic-minimal-polynomial-4x4

Problem

Let

A

be the

4 \times 4

real matrix

A = \begin{bmatrix} 1 & 1 & 0 & 0 \\ -1 & -1 & 0 & 0 \\ -2 & -2 & 2 & 1 \\ 1 & 1 & -1 & 0 \end{bmatrix}.

Show that the characteristic polynomial for

A

x^2(x-1)^2

and that it is also the minimal polynomial.