Diagonal matrices and diagonalizability are key topics in linear algebra as well as numerical linear algebra. Likewise, symmetric matrices have lots of nice properties that make them widely studied and important both theoretically and computationally.
However, anti-diagonal matrices seem to be no more than a curiosity in matrix algebra. While symmetry along the main diagonal seems to count for so much, persymmetry does not seem to count for very much at all.
Is there a reason for this? After all (and this might sound naive) why should one diagonal (left to right) matter so much more than the other one? Is this an artifact / convention arising from the development of matrix algebra or does it reflect something deeper.
Or, are anti-diagonal and per-symmetric matrices of far greater importance than I think?
I was thinking about this and was not really able to come up with anything close to a satisfactory answer.
