ECEN601_hw10_pfister

ECEN601_hw10_pfister - A then 1/Î is an eigenvalue of A-1...

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ECEN 601: Assignment 10 Problems: 1. Show that the determinant of an n × n matrix is the product of the eigenvalues; that is, det( A ) = n productdisplay i =1 λ i . 2. Show that the trace of a matrix is the sum of the eigenvalues, tr( A ) = n summationdisplay i =1 λ i . 3. Show that if λ * is an eigenvalue of A , then λ * + r is an eigenvalue of A + rI , and that A and A + rI have the same eigenvectors. 4. Suppose that A - 1 exists; prove the following statements. If
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Unformatted text preview: A then 1 /λ is an eigenvalue of A-1 . The eigenvectors of A corresponding to nonzero eigenvalues are eigenvectors of A-1 . 5. Show that the eigenvalues of a projection matrix P are either 1 or 0. 6. Determine the Jordan forms of A 1 = 2 1 2 2 3 2 and A 2 = 2 2 2 3 2 . 1...
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