16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.2.7

The Rational and Jordan Forms

Mathematics — Linear Algebra · minimal-polynomial-rational-form

Problem

Find the minimal polynomials and the rational forms of each of the following real matrices.

\begin{bmatrix} 0 & -1 & -1 \\ 1 & 0 & 0 \\ -1 & 0 & 0 \end{bmatrix}, \qquad \begin{bmatrix} c & 0 & -1 \\ 0 & c & 1 \\ -1 & 1 & c \end{bmatrix}, \qquad \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}.