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Mathematics-Online course: Linear Algebra - Normal Forms - Eigenvalues and Eigenvectors

Similarity Transformation

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The eigenvalues remain unchanged under similarity transformation

$\displaystyle A \to B = Q^{-1}AQ\, . $

The eigenvectors are transformed according to the change of basis described by $ Q$. That is, An eigenvector $ w$ of $ A$ associated with eigenvalue $ \lambda$ corresponds to eigenvector $ v = Q^{-1}w$ of $ B$ associated with the same eigenvalue.
(Authors: Burkhardt/Höllig/Hörner)

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  automatically generated 4/21/2005