So I know the properties that $A^T = A$ if its orthogonally diagonalizable and also $A=PDP^T$, But cant quite use them to prove or disprove. Would appreciate any help.
2026-03-28 14:06:34.1774706794
Prove or Disprove: If $A$ and $ B$ are $n \times n$ orthogonally diagonalizable matrices, then $A + B$ is orthogonally diagonalizable.
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If $A^T=A$ and $B^T=B$, then $(A+B)^T=A^T+B^T=A+B$.