Does the standard euclidean metric on $\mathbb{R}^{k^2}$ refer to $$ \left(\sqrt{\sum_{i=1}^{k}x_i^2}\right)^2 = \sum_{i=1}^{k}x_i^2 $$
or does $\mathbb{R}^{k^2}$ have some other meaning, like $\mathbb{R}^k \times \mathbb{R}^k$?
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4In typical notation $\mathbb{R}^k\times \mathbb{R}^k = \mathbb{R}^{2k}$ and $\mathbb{R}^{k^2} = \mathbb{R}^k\times \ldots \times \mathbb{R}^k$ ($k$ times) or $\mathbb{R} \times \ldots \times \mathbb{R}$ ($k^2$ times). – Winther Jan 28 '15 at 21:07
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2most common use is for square matrices, the (squared) norm is $\operatorname{trace} A^T A$ – Will Jagy Jan 28 '15 at 21:16
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@Winther got it. – Mr.Young Jan 28 '15 at 23:07
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@WillJagy Thanks – Mr.Young Jan 28 '15 at 23:07