Can't we create an orthogonal basis for a matrix A as long as A is diagonalizable? Does A have to be symmetric for it to be orthogonally diagonalizable?
2026-03-29 12:40:40.1774788040
Are only symmetric matrices orthogonally diagonalizable?
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Suppose that we are working with real matrices, and we can write $A=U^TDU$
Then $A^T=U^TD^T(U^T)^T=U^TDU=A$