But something has to be written on the birth certificate and social security card, and that’s what everything else will expect you to use. I think just due to technical limitations (e.g. of the printer/template for those things) it wouldn’t be allowed, but I dunno about legally
The eigenvalues of a diagonal matrix are the values on the diagonal. Diagonalizable matrices’ eigenvalues can be determined by diagonalizing them and looking at the entries on the diagonal.