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We prove the following statement from the wonderful world of linear algebra: Every symmetric matrix with only eigenvalues 1 and -1 is orthogonal. In another video: Every orthogonally diagonalizable matrix is symmetric: • Every orthogonally diagonalizable mat... matrix, linear algebra, linear, algebra, symmetric, symmetric, eigenvalue, eigenvalues, 1 and -1, orthogonal, diagonal, diagonalizable, proof, exercise, solution, exam, state exam, test, principal axis, transformation, principal axis transformation, conjugated, transposed, diagonal matrix