hw8-solutions

B the eigenvalues of are all positive by theorem 5

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Unformatted text preview: heorem 5. Since the eigenvalues of are the reciprocals of eigenvalues of (see Exercise 25 in section 5.1), the eigenvalues of are positive (also it can easily be shown that is symmetric), by theorem 5, the quadratic form is positive definite. Problem 4. For a given quadratic form given by a quadratic polynomial Step 1. Find the corresponding symmetric matrix Step 2. Find the eigenvalues of : s.t. and sort them in decreasing order Step 3. For each eigenvalue find the unit eigenvectors corresponding to Step 4. Based on theorem 6, any of those unit eigenvectors...
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This note was uploaded on 02/13/2014 for the course CS 132 taught by Professor Kfoury during the Fall '13 term at BU.

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