Difference between revisions of "Normal matrix"
From Encyclopedia of Mathematics
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| − | A square [[ | + | A square complex [[matrix]] $A$ that commutes with its [[adjoint matrix]] $A^*$: that is, $AA^*=A^*A$. |
====Comments==== | ====Comments==== | ||
| − | See also [[Normal operator| | + | See also [[Normal operator]]. |
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| + | The [[eigenvector]]s of a normal matrix form an [[orthonormal system]]. A matrix $A$ is normal if and only if it is unitarily [[Similar matrices|similar]] to a [[diagonal matrix]]: $\Delta = U^{-1} A U$ with $u$ a [[unitary matrix]]. | ||
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| + | ====References==== | ||
| + | * Lloyd N. Trefethen, David Bau III, ''Numerical Linear Algebra'' SIAM (1997) ISBN 0898713617 | ||
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| + | [[Category:Special matrices]] | ||
Revision as of 21:00, 17 October 2014
A square complex matrix $A$ that commutes with its adjoint matrix $A^*$: that is, $AA^*=A^*A$.
Comments
See also Normal operator.
The eigenvectors of a normal matrix form an orthonormal system. A matrix $A$ is normal if and only if it is unitarily similar to a diagonal matrix: $\Delta = U^{-1} A U$ with $u$ a unitary matrix.
References
- Lloyd N. Trefethen, David Bau III, Numerical Linear Algebra SIAM (1997) ISBN 0898713617
How to Cite This Entry:
Normal matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_matrix&oldid=32547
Normal matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_matrix&oldid=32547