Kunze Linear Algebra · Problem 7.1.2

Rational and Jordan Forms

Mathematics — Methods · cyclic-subspaces

Problem

Let TT be the linear operator on R3R^3 which is represented in the standard ordered basis by the matrix [20002000−1].\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & -1 \end{bmatrix}. Prove that TT has no cyclic vector. What is the TT-cyclic subspace generated by the vector (1,−1,3)(1, -1, 3)?

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