$A\in \text{Mat}_n(\mathbb{R})$, where $A$ is a matrix.
Thanks for your help. I try google it but found nothing.
If it is not hard for you, explain please the definition of this notation.
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4$\begingroup$ It might be that $Mat_n(R)$ stands for $\mathbb R^{n\times n}$, that is, the set of $n\times n$ matrices with real entries. $\endgroup$– FimpellizzeriCommented Dec 5, 2018 at 6:10
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$\begingroup$ @Fimpellizieri $Mat_n(\mathbb{R})$, the set of $n\times n$ matrices, and $\mathbb{R}^{n^2} $, are not identical spaces. They are isomorphic as vector spaces, but they are different. $\endgroup$– AnonymousCowardCommented Dec 5, 2018 at 6:12
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1$\begingroup$ $\Bbb R^{n\times n}$ is not the same as $\Bbb R^{n^2}$ as I've learned it. The former refers to $n\times n$ matrices with entries in $\Bbb R$ while the latter refers to vectors with $n^2$ entries in $\Bbb R$. $\endgroup$– FimpellizzeriCommented Dec 5, 2018 at 6:16
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1 Answer
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$\text{Mat}_n(R)$ stands for all square matrices in $\mathbb{R}^{n \times n}$ as seen in "Linear Time-Varying Systems: Algebraic-Analytic Approach".
So $\mathbf A \in \text{Mat}_n(R)$ is simply another way of denoting $\mathbf A \in \mathbb{R}^{n \times n}$. Similarly, $\mathbf A \in \text{Mat}_{\infty}(R)$ would be a $\infty \times \infty$ dimensional matrix.
$$ \mathbf A = \begin{bmatrix} a_{11} & a_{12} & ... \\ a_{21} & a_{22} & ... \\ \vdots & \vdots & \ddots \end{bmatrix} $$
