Orthogonally Diagnolizable matrix
Let us say matrix \(A\) is diagnolizable. We say that A is orthogonally diagnolisable if and only if \(S\) is orthogonal, i.e., \(SS^T=I\) or \(S^{-1}=S^T,\) i.e.,
\[
S^{-1}AS=B \text{ becomes } S^TAS=B
\]
Important Points to Note
- The matrix \(A\) must be real symmetric matrix to be orthagonally diagnolizable.