Matrix with the same value in all entries — which notation to use? Pretty trivial but for a matrix
\begin{bmatrix}x&x&\ldots&x&x\\x&x&\ldots&x&x\\\vdots&\vdots&\ddots&x&x\\x&x&\ldots&x&x\end{bmatrix}
with  $N\times N $, is there is simpler notation. I had $A=[x_{i,j}]\in \Bbb R^{N\times N}$ in my mind, but I can't find anywhere were it is used
Edit: I forgot to mention but, I need to work with the elements in the matrix, so like doing scalar multiplication (to do a proof by the principle of mathematical induction question). But it a $3\times 3$ so I figured out I do have to write every single element 9 times in a row. Is there any notation that can make my math simpler?
 A: It is common for $J$ or $J_{n}$ to be used as a square ($n \times n$) matrix of all 1s, though not so common that you shouldn't specify that this is what you mean. You can also write $J_{m,n}$ for an $m \times n$ matrix of all ones.  It is also common for ${\bf{j}}$ to be used for a vector of all ones.
These all ones matrices and vectors come up in a variety of situations in algebra and combinatorics; for example

*

*$J_{n}-I_{n}$ is the adjacency matrix for the complete graph $K_{n}$

*$J_{m,n}$ is the identity element for the set of $m\times n$ matrices under the Hadamard product;

*the proof of Fisher's Inequality for combinatorial designs relies on the fact that the incidence matrix of such a structure must satisfy the equation $B^{T}B=(r-\lambda)I+\lambda J$ (where $r$ and $\lambda$ are parameters of the design).

A: Assuming that $x \neq 0$, it's a rank-$1$ matrix. Thus, to emphasize its rank-$1$-ness, I would use
$$\color{blue}{x \,{\Bbb 1}_n {\Bbb 1}_n^\top}$$
A: I don't think there is a common notation, as this type of matrix isn't extremely common. However in Statistics I have seen a column or matrix of ones written as a $J$.
