Kunze Linear Algebra · Problem 7.2.8

Rational and Jordan Forms

Mathematics — Methods · cyclic-decomposition

Problem

Let TT be the linear operator on R3R^3 which is represented in the standard ordered basis by [3−4−4−1322−4−3].\begin{bmatrix} 3 & -4 & -4 \\ -1 & 3 & 2 \\ 2 & -4 & -3 \end{bmatrix}. Find non-zero vectors α1,…,αr\alpha_1, \ldots, \alpha_r satisfying the conditions of Theorem 3.

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