Find%20EIGENVALUES%20and%20EIGENVECTORS%20for%20the%20matrix:

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Find EIGENVALUES and EIGENVECTORS for the matrix
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2
-1
The EIGENVALUES are
and
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has EIGENVALUES 2 and -1 and
EIGENVECTORS
Cosets of eigenspace??
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has EIGENVALUES 2 and -1 and
EIGENVECTORS
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W
Add the same vector
to every point on W
to get a COSET OF W
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W
Add the same vector
to every point on W
- a line parallel to W
to get a COSET OF W
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W
The COSETS of the EIGENSPACE W are lines
parallel to W.
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W
The blue coset can be obtained by adding the
vector
to each vector in W
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W
The blue coset can be obtained by adding the
vector
to each vector in W
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If v is a vector in the blue coset then v k

W
The blue coset can be obtained by adding the
vector
to each vector in W
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W
v
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W
Av kA A
A vector on W
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W
Every point on the blue coset has an image on
the green coset.
Av kA A
A vector on W
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Consider the EIGENSPACE W
If v is a vector in the blue coset then v k

W
Av kA A
A vector on W
If B is a coset of an eigenspace W then A maps
every point on B onto G , another coset of W.