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P and Q are two Hermitian matrices and there exists a matrix R, which diagonalizes both of them, such that RPR =S, and RQR = S, , where S, and S, are diagonal matrices. The correct statement(s) is (are) (a) All the elements of both matrices S, and S, are real (b) The matrix PQ can have complex eigenvalues. (c) The matrix QP can have complex eigenvalues. (d) The matrices P and Q commute

P and Q are two Hermitian matrices and there exists a matrix R, which diagonalizes both of them, such that RPR =S, and RQR = S, , where S, and S, are diagonal matrices. The correct statement(s) is (are) (a) All the elements of both matrices S, and S, are real (b) The matrix PQ can have complex eigenvalues. (c) The matrix QP can have complex eigenvalues. (d) The matrices P and Q commute

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P and Q are two Hermitian matrices and there exists a matrix R, which diagonalizes -1 both of them, such that RPR = S, and RQR = S, , where S, and S, are diagonal matrices. The correct statement(s) is (are) (a) All the elements of both matrices S, and S, are real (b) The matrix PQ can have complex eigenvalues. (c) The matrix QP can have complex eigenvalues. (d) The matrices P and Q commute
Transcribed Image Text:P and Q are two Hermitian matrices and there exists a matrix R, which diagonalizes -1 both of them, such that RPR = S, and RQR = S, , where S, and S, are diagonal matrices. The correct statement(s) is (are) (a) All the elements of both matrices S, and S, are real (b) The matrix PQ can have complex eigenvalues. (c) The matrix QP can have complex eigenvalues. (d) The matrices P and Q commute
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