# Notation: Rows and Columns of Matrix

A purely notational question:

It is possible to denote the rows of a matrix $\mathbf{A}\in\mathbb{R}^{n\times m}$ by $\mathbf{w_1},\ldots,\mathbf{w_n}\in\mathbb{R}^{1\times m}$ and the columns by $\mathbf{v_1},\ldots,\mathbf{v_m}\in\mathbb{R}^{1\times n}$, such that $$\mathbf{A}=\left(\begin{matrix}\mathbf{w_1}\\\vdots\\\mathbf{w_n}\end{matrix}\right)=\left(\begin{matrix}\mathbf{v_1}&\cdots&\mathbf{v_m}\end{matrix}\right).$$

Now, I write a paper containing a lot of matrices and in which I have to talk a lot about their rows. Thus instead of $\mathbf{w_k}$, I conveniently used the notation $\mathbf{A_k}$ to denote the $k^{th}$ row of $\mathbf{A}$, which has the big advantage that it is immediately clear of which matrix $\mathbf{A_k}$ is the $k^{th}$ row.

However, I also sometimes have to talk about the columns of $\mathbf{A}$, which were denoted by $\mathbf{v_l}$ above. Denoting them by $\mathbf{A}_l$ is not an option, since this already denotes the $l^{th}$ row. Giving them a completely different name neither, since this makes the paper ugly and hard to read. What I would like is a clean notation to denote either rows or columns which still associates the rows/columns with $\mathbf{A}$. I thought of $\mathbf{A}_{*,l}$ and $\mathbf{A_{k,*}}$, but some matrix names already contain sub- and super-scripts themselves, making this notation ugly, too. In short, I need a notation for the rows respectively columns which would look also nice for e.g. $\mathbf{A_\beta^i}(t)\in\mathbb{R}^{n\times m}$. It would be OK if the notation would be nicer for the rows than for the columns, since I talk about the latter less often.

• You could go with $A^{(i)}$ for "i-th column of matrix $A$". Or simply $A^i$, if you never deal with powers of matrices. Just make sure the reader knows what's happening. – 5xum Jan 21 '16 at 15:00
• Tagging onto your initial proposal for names, what do you think of $A_{\cdot l}$ for the $l$th column and $A_{k \cdot}$ fro the $k$-th row? Depending on sup- and sub-scrips, you could also go with a bracketed version: $(\mathbf{A_\beta^i}(t))_{\cdot l}, (\mathbf{A_\beta^i}(t))_{k\cdot }$. If the ´\cdot´ is too subtle for your taste, also $(\mathbf{A_\beta^i}(t))_{* l}$ and $(\mathbf{A_\beta^i}(t))_{k*}$ might work. – Roland Jan 21 '16 at 15:29
• $A^i$ or $A^{(i)}$ won't work since $A^i$ is already denoting $A$ at iteration $i$ (it's an iterative method). I would also like to avoid additional brackets, since there are already too many of them in the equations... – Engineer trying math Jan 21 '16 at 15:43
• This is an excellent question. It is a pity that there is no standard notation. As a special example, it would be very useful to have a standard notation for the columns of the identity matrix. – wdacda May 18 '18 at 9:59