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Let $X \in \mathbb{R}^{N\times T}$, where $N,T\in \mathbb{Z}^{> 0}$, and $x\in (\mathbb{R}^N)^T$, by which I mean $x = (x_1, x_2, \dots, x_T)$, where $x_i \in \mathbb{R}^N$. The objects $X$ and $x$ are different representations of the same thing. Is it incorrect, or strange, write $X\in (\mathbb{R}^N)^T$ or $x\in \mathbb{R}^{N\times T}$? Are there alternative ways to connect these two representations?

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