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(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 nonsymmetric 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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 Fall '13
 KFOURY
 Algorithms

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