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Exercise 8.D.5

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Proof. By Exercise 9 in section 8B we just need to square each block on the diagonal of the Jordan form of $T$ . In other words, the matrix of $T^{2}$ is a block diagonal matrix where each block has the following form

{(\begin{matrix} λ_{j} & 1 & 0 \\ ⋱ & ⋱ \\ ⋱ & 1 \\ 0 & λ_{j} \end{matrix})}^{2} = (\begin{matrix} λ_{j}^{2} & 2 λ_{j} & 0 \\ ⋱ & ⋱ \\ ⋱ & 2 λ_{j} \\ 0 & λ_{j}^{2} \end{matrix}) .

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celiopassos

2017-10-06 00:00

Exercise 8.D.5

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