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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

  1. The matrix \(A\) must be real symmetric matrix to be orthagonally diagnolizable.