Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given that $\mathbb{R}^n$ is the notation used for n-dimensional vectors, is there an accepted equivalent notation for matrices?

share|cite|improve this question
up vote 6 down vote accepted

If $A$ is an $m\times n$ matrix, then $$A \in \mathbb{R}^{m\times n}$$

share|cite|improve this answer
1  
Since $\times$ is the official symbol for multiplying integers, this notation is in principle ambiguous: $2\times3=6$ would seem to imply $\Bbb R^{2\times 3}=\Bbb R^6$, but the latter is not a space of matrices. I agree that this is nitpicking, and would apply to the term "$m\times n$ matrix" itself too, but I personally prefer notations which use a comma rather than $\times$ (or nothing) between $m$ and $n$ (and this applies to matrix subscripts as well). – Marc van Leeuwen Oct 29 '13 at 10:30
    
I agree. If you just wrote $A\in \mathbb{R}^{m\times n}$ it wouldn't be necessarily clear $A$ is a matrix. – dezign Aug 20 '15 at 5:25

As you can see from the previous two answers, several notations are in common usage, so it's best to say what you mean the first time you use it to be completely clear. (For what it's worth, I often use $M_{m\times n}(\mathbb{R})$, which is different again).

share|cite|improve this answer
    
Does your notation refer to $m \times n$ or to $n \times m$ matrices? (The OP asks for $m \times n$.) – Ryan Oct 29 '13 at 4:31
    
@Ryan Thanks - force of habit. – Matthew Pressland Oct 29 '13 at 9:44
    
Np, I asked because my textbook just did the same thing, and it got me confused (thus ending up here after searching for the answer). – Ryan Oct 29 '13 at 13:10

The vector space of real matrices with $n$ rows and $m$ columns is denoted by $\mathcal{M}_{n,m}(\mathbb R)$ and its $nm$-dimensional vector space so it's isomorphic to $\mathbb R^{nm}$

share|cite|improve this answer
    
Oh, I did not pay attention to what the OP wrote and yet I think my answer does not make confusion. – user63181 Oct 29 '13 at 14:03

The notation $A\in\mathbb{R}^{m\times n}$ is in fact correct. We should be careful with the symbol '$\times$' that in this case does not means an integer product but a group product that, as a result, is a new group in $\mathbb{R}^2$ with elements of the form $(m, n)$, and thus the matrix $A$ is contained in it.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.