Conventional notation for this matrix operation

Question

Given some binary adjacency matrix $A$ and index $n$, define matrix $B$ such that $$B_{ij} = \begin{cases} 1 & \text{if $(A^n)_{ij} \geq 1$} \\ 0 & \text{if $(A^n)_{ij} < 1$} \end{cases}$$

e.g. $$A = \begin{pmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \end{pmatrix}, n=2, \qquad \text{then} \qquad B = \begin{pmatrix} 1 & 0 & 1 \\ 1 & 1 & 1 \\ 1 & 0 & 1 \end{pmatrix}$$

Is there an established notation instead of using $f(A^n) = B$?

Answer 1

Using Boolean algebra, then $\rm{B} = \rm{A}^2$.

$$\rm{A}^2 = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 1 \\ 1 & 1 & 1 \\ 1 & 0 & 1 \end{bmatrix} = {\rm B}$$