Unformatted text preview: λ 1 + λ 2 equals trM , and that λ 1 λ 2 equals detM (the two invariants of M ). For the second matrix, what conditions on b and c will make M positive deﬁnite? 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 = Σ x i ¯ y i 7. Keener 1.2.5 (p.51) 8. If A and B are positive deﬁnite matrices and Ax = λBx , where λ is a scalar, show that λ must be positive....
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 Fall '04
 BELMONTE
 Linear Algebra, Applied Mathematics, Matrices, Vector Space, inner product, order polynomials, valid inner product, linear vector spaces

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