17 If A is n*n matrix with real entries,then
(a) A has n eigenvalues exactly.
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18 If A can be QR factorized,then
(a) A has linearly independent eigenvectors.
(b) The columns of Q are orthonormal basis for ColA.
(c)(Q^T)*Q=I.
(d)A=QR and (Q^T)*Q=I => (Q^T)*A = (Q^T)*Q*R => (Q^T)*A = R =>Q*(Q^T)*A = QR = A =>Q(Q^T) = I.
(e)R is an upper triangular invertible matrix with positive entries on its upper triangel.
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