16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.2.1

The Rational and Jordan Forms

Mathematics — Linear Algebra · cyclic-decompositions

Problem

Let TT be the linear operator on F2F^2 which is represented in the standard ordered basis by the matrix [0010].\begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix}. Let α1=(0,1)\alpha_1 = (0, 1). Show that F2≠Z(α1;T)F^2 \neq Z(\alpha_1; T) and that there is no non-zero vector α2\alpha_2 in F2F^2 with Z(α2;T)Z(\alpha_2; T) disjoint from Z(α1;T)Z(\alpha_1; T).

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