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# Notation for the set of m by n matrices

Put content here**Notation for the set of $m \times n$ matrices:** The set of all $m \times n$ matrices with entries from a field $\mathbb{F}$ is denoted by:
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$$M_{m \times n}(\mathbb{F}) \quad \text{or} \quad \mathbb{F}^{m \times n} \quad \text{or} \quad \text{Mat}_{m \times n}(\mathbb{F})$$
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Common special cases:
- $M_{m \times n}(\mathbb{R})$ or $\mathbb{R}^{m \times n}$: real $m \times n$ matrices
- $M_{m \times n}(\mathbb{C})$ or $\mathbb{C}^{m \times n}$: complex $m \times n$ matrices
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When $m = n$, we write $M_n(\mathbb{F})$ or $\mathbb{F}^{n \times n}$ for the set of $n \times n$ square matrices.
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This set forms a **vector space** over $\mathbb{F}$ of dimension $mn$ under matrix addition and scalar multiplication.

# Parents

* Basic terminology and notation