# How do you write / represent the 'all ones matrix'?

Is there a convention to write the all ones matrix in formulas? I'm going to write about the following formular:

$$A = B + XD + DX + N$$

Where D is a diagonal matrix and X the all ones matrix:

$$X = \begin{pmatrix} 1 & 1 & \cdots & 1 \\ 1 & 1 & \cdots & 1 \\ \vdots & \vdots & \ddots & \vdots \\ 1 & 1 & \cdots & 1 \end{pmatrix}$$

Is there a greek letter or other convention?

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You could write $\mathbf1\mathbf1^\top$, where $\mathbf1$ is the vector with all components $1$. – joriki Feb 18 '13 at 19:19
I have seen it written as J, for example, by people who discuss incidence matrices of projective planes. The incidence matrix $A$ of a projective plane of order $n$ satisfies $A^{t}A = AA^{t} = nI +J,$ and $AJ = JA = nJ.$ – Geoff Robinson Feb 18 '13 at 19:23
Mathworld and Wikipedia both seem to use $J$. I'm not sure if this is a set convention though since this overlaps with notation for the Jordan form. – EuYu Feb 18 '13 at 19:24
Unit matrix "J" will do. Thank you! – edgar.holleis Feb 18 '13 at 19:33

Yes, I have seen the $n\times n$ all-ones matrix denoted $J_n$. I think this is somewhat conventional in algebraic combinatorics, but I have no idea whether it is commonly used elsewhere.