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Unformatted text preview: 1 + 2 equals trM , and that 1 2 equals detM (the two invariants of M ). For the second matrix, what conditions on b and c will make M positive denite? 4. Keener 1.2.4 (p.51) 5. If A is a Hermitian matrix, show that 1) all eigenvalues are real, 2) if two eigenvalues are distinct, then the corresponding eigenvectors are orthogonal. 6. Show that A * = A T for h x, y i = x i y i 7. Keener 1.2.5 (p.51) 8. If A and B are positive denite matrices and Ax = Bx , where is a scalar, show that must be positive....
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 Fall '04
 BELMONTE
 Applied Mathematics, Matrices, Vector Space

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