eigenvector

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eigenvector
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Domain Range
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Domain Range
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eigenvector
Domain Range
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Domain Range
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definition T is a linear transformation ,

EIGENVECTOR
EIGENVALUE
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A is the matrix for a linear transformation
T relative to the STANDARD BASIS
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T
T
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The matrix for T relative to the ? basis
T
T
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The matrix for T relative to the ? basis
Diagonal matrix
Eigenvectors for T
T
T
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The matrix for a linear transformation T
relative to
a basis of eigenvectors
will be diagonal
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To find eigenvalues and eigenvectors for a given
matrix A
Solve for and
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To find eigenvalues and eigenvectors for a given
matrix A
Solve for and
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det

det
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det

det
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det

det
This is called the characteristic polynomial
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det

det
0
the eigenvalues are 2 and -1
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the eigenvectors belonging to 2 are nonzero
vectors in the null space of 2I - A
2
A )
I
(
-

the null space of 2I - A
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the eigenvectors belonging to -1 are nonzero
vectors in the null space of -1I - A
-1
A )
I
(
-

the null space of -1I - A
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Matrix for T relative to standard basis
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Matrix for T relative to columns of P
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Basis of eigenvectors
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eigenvalues