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Mathematics-Online course: Linear Algebra - Normal Forms - Diagonalisation

Unitary Diagonalisation of Normal Matrices

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A matrix $ A$ is normal if and only if $ A$ is unitarily diagonalisable, that is, if

$\displaystyle U^{-1} A U = \operatorname{diag}(\lambda_1,\ldots,\lambda_n) \,, $

where the columns of $ U$ form an orthonormal basis consisting of eigenvectors associated with eigenvalues $ \lambda_j$.

(Authors: App/Burkhardt/Höllig/Kimmerle)

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  automatically generated 4/21/2005