We can define an infinite diagonal matrix with some ease, and then say that a finite diagonal matrix is the top left sub-matrix of our infinite one.
Can we define an infinite anti-diagonal matrix? It seems more like a facet of the indexing system than anything else, but where we can refer to the "top left" term for a matrix of any size, I don't see a way to reference the "bottom left" term, if there is no bottom.
I'll note that we can still say that
A[i,j] = A[i-1,j+1]
An anti-diagonal matrix of any finite size is trivial to define; does it not exist as an infinite matrix?