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Let \(L: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}\) be a linear map with the property that \(L \mathbf{v} \perp \mathbf{v}\) for every \(\mathbf{v} \in \mathbb{R}^{3}\).

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Let \(L: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}\) be a linear map with the property that \(L \mathbf{v} \perp \mathbf{v}\) for every \(\mathbf{v} \in \mathbb{R}^{3}\). Prove that \(L\) cannot be invertible.
Is a similar assertion true for a linear map \(L: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\) ?
in Mathematics by Platinum (101k points) | 444 views

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