Mathematics-Online lexicon: Diagonalisation of Hermitian Matrices

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	Mathematics-Online lexicon:
	Diagonalisation of Hermitian Matrices

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 $\lambda_i$ of a hermitian matrix $A \; (A=A^*)$ are real, and there exists an ONB consisting of eigenvectors

. Therefore

$\displaystyle U^*AU=$ diag $\displaystyle (\lambda_1,\ldots,\lambda_n)\,,$

where $U=(v_1,\ldots,v_n)$ is an unitary matrix.

The special case of real symmetric matrices $(A=A^{\operatorname t})$ provides real eigenvalues.

(Authors: Höllig/Reble/Höfert)

Example:

automatically generated 2/ 9/2005