Say I have a real $m \times n$ matrix $\mathbf{M}$. Shall I write $\mathbf{M} \in \mathbb{R}^{m \times n}$ or $\mathbf{M} \in \mathbb{R}^{m,n}$?
What is commonly accepted and most beautiful and correct version?
Moreover, shall I use an italic bold font like $\boldsymbol{M}$ or vertical bold $\mathbf{M}$? And same question for vectors: I personally dislike $\mathbf{x}$ and prefer $\boldsymbol{x}$. What is commonly and beautifully accepted?
In conclusion, if I got it right, $\boldsymbol{M}\in\mathbb{R}^{m \times n}$ and $M_{i,j}\in\mathbb{R}$.
Best Answer
I see this very often and was taught this: $$M_{m,n}(\mathbb{R})$$ If it's just a square matrix, then $$M_n(\mathbb{F})$$ where $\mathbb{F}$ is an arbitrary field. These are the sets of matrices. For an arbitrary matrix, say like your example. Then I would see $$\mathbf{A}\in{M_{m,n}(\mathbb{F})}$$ where $\mathbf{A}$ is your matrix. I like the bold personally, but it is not required I don't believe.