So far, all we are doing in class is determine if the matrix A is symmetric, find the basis for the eigenspace P, and apply Gram Schmidt for it to be orthogonal. My question is; why must A be symmetric in the first place?
In the end of the day, we will still apply Gram Schmidt to solve for orthogonal matrices - wont that mean that the inverse of P is the transpose? Does that imply A wont produce a diagonal matrix if it wasn't symmetric? Any idea why?