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. That is, each point is an eigenvector of corresponding to eigenvalue (b) Suppose rotates points about some line that passes through the origin in . That line
consists of all multiples of some nonzero vector . The points on this line do not move under
the action of , then
. Thus is and eigenvector of corresponding to eigenvalue .
The eigenspace is Span .
If rotation happens to be half of a full rotation, that is, through and angle of 180 degrees, let
be a plane through the origin that is prependecular to line . Each point in the pl...
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- Fall '13
- Algorithms, Eigenvalue, eigenvector and eigenspace, Orthogonal matrix, Saber Mirzaei, matrix iff