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Exercise 2.7.4

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$A = [\begin{matrix} 0 & 1 \\ 0 & 0 \end{matrix}]$ has $A^{2} = 0 .$ But the diagonal of $A^{T} A$ has dot products of columns of $A$ with themselves. If $A^{T} A = 0$ , zero dot products $\Rightarrow$ zero columns $\Rightarrow A =$ zero matrix.

mathchakra

2021-12-20 21:26

Exercise 2.7.4

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