Mathematics-Online lexicon: Eigenvalues and Eigenvectors under Similarity Transformations

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematics-Online lexicon:
	Eigenvalues and Eigenvectors under Similarity Transformations

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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

. That is, An eigenvector

associated with eigenvalue $\lambda$ corresponds to eigenvector $v = Q^{-1}w$ of

associated with the same eigenvalue.

(Authors: Burkhardt/Höllig/Hörner)

Annotation:

automatically generated 2/ 9/2005