# Normal matrix

From Encyclopedia of Mathematics

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