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* [[hermitian matrix|Hermitian]] or self-adjoint if ''A'' = ''A''<sup>*</sup>;
* [[skew-Hermitian matrix|skew Hermitian]] if ''A'' = -''A''<sup>*</sup>;
* [[normal matrix|normal]] if ''A<sup>*</
Even if ''A'' is not square, the two matrices ''A<sup>*</sup>A'' and ''AA<sup>*</sup>'' are both Hermitian and in fact [[positive semi-definite]].
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