# What the meaning of $\text{Mat}_n(\mathbb{R})$

$$A\in \text{Mat}_n(\mathbb{R})$$, 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.

• 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. Commented Dec 5, 2018 at 6:10
• @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. Commented Dec 5, 2018 at 6:12
• $\Bbb R^{n\times n}$ 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 $\Bbb R$. Commented Dec 5, 2018 at 6:16

## 1 Answer

$$\text{Mat}_n(R)$$ 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.

$$\mathbf A = \begin{bmatrix} a_{11} & a_{12} & ... \\ a_{21} & a_{22} & ... \\ \vdots & \vdots & \ddots \end{bmatrix}$$