Kunze Linear Algebra · Problem 7.2.7

Rational and Jordan Forms

Mathematics — Methods · rational-form

Problem

Find the minimal polynomials and the rational forms of each of the following real matrices. [0−1−1100−100],[c0−10c1−11c],[cos⁡θsin⁡θ−sin⁡θcos⁡θ].\begin{bmatrix} 0 & -1 & -1 \\ 1 & 0 & 0 \\ -1 & 0 & 0 \end{bmatrix}, \quad \begin{bmatrix} c & 0 & -1 \\ 0 & c & 1 \\ -1 & 1 & c \end{bmatrix}, \quad \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}.

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