hw8-solutions

Based on theorem 6 any of those unit eigenvectors

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Unformatted text preview: maximize (a) Following the steps explained above, the solution is the set of unit eigenvectors corresponding to eigenvalue which are [ (b) Following the steps explained above, we find two base unit vectors for [ √ √ ] and [ √ √ which are , so any linear combination of these two vectors can be a solution. Problem 5. (a) (a.1) (a.2) so is symmetric {} → Hence is skew negative definite. (b) For any non-symmetric matrix , is a quadratic polynomial in dimensional space. At the same time from problem one, we know that any quadratic polynomial can be transformed in to a matrix multiplication form s.t. for some symmetric matrix . Hence is a quadratic form....
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