Unformatted text preview: the same steps we get:
[ Problem 5.
(a) ̂ ( ) (b) Any vector in
( ) has the form
, use exercise 28 since is symmetric: ( )( ) →
for some . To show that →
̂ is orthogonal to [(
[
(
̂)
̂)]
̂ is in
(
). So
, and the
̂(
̂) express as the sum of a vector in and a vector in
decomposition
.
By the orthogonal decomposition theorem in section 6.3, this decomposition is unique, and so
̂ must be Problem 6.
(a) For [ the eigenvalues are and . Corresponding eigenvectors will be the solutions for
For [ For [ ] the nor...
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 Fall '13
 KFOURY
 Linear Algebra, Algorithms, Eigenvectors, orthogonal projection, Saber Mirzaei

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