How can I get A knowing Ap and p?

For an n*n symbolic matrix A and an n*1 symbolic vector p, if I know the value of p and Ap, how can I find A?

Answer 1

[John D'Errico]

No. There is insufficient information. You can view this as knowing n pieces of information, but needing to output n^2 pieces of information. (Since the nxn matrix A has n^2 elements.) So there are infinitely many possible matrices A that would generate the given result, and you cannot resolve which of those infintely many possible solutions actually form the real matrix A.