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Normal matrix

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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://www.encyclopediaofmath.org/index.php?title=Normal_matrix&oldid=33757