Conjugate transpose: Difference between revisions

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* A [[wp:Hermitian matrix|Hermitian matrix]] equals its own conjugate transpose: &nbsp; <big><math>M^H = M.</math></big>
* A [[wp:normal matrix|normal matrix]] is commutative in [[matrix multiplication|multiplication]] with its conjugate transpose: &nbsp; <big><math>M^HM = MM^H.</math></big>
* A [[wp:unitary matrix|unitary matrix]] has its [[inverse matrix|inverse]] equal to its conjugate transpose: &nbsp; <big><math>M^H = M^{-1}.</math></big> <br> This is true when: <br> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[wikt:iff|'''iff''']] &nbsp; <math> M^HM = I_n </math> &nbsp; and <br> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[wikt:iff|'''iff''']] &nbsp; <big><math>MM^H = I_n,</math></big> &nbsp; where &nbsp; <big><math>I_n</math></big> &nbsp; is the identity matrix.
 
 
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