Conjugate transpose: Difference between revisions
Content deleted Content added
Formulate had been invisible on OS X browsers (Safari, Chrome) - removing flanking white space in math tags seems to fix this ... |
No edit summary |
||
Line 15: | Line 15: | ||
* A [[wp:Hermitian matrix|Hermitian matrix]] equals its own conjugate transpose: <big><math>M^H = M.</math></big> |
* A [[wp:Hermitian matrix|Hermitian matrix]] equals its own conjugate transpose: <big><math>M^H = M.</math></big> |
||
* A [[wp:normal matrix|normal matrix]] is commutative in [[matrix multiplication|multiplication]] with its conjugate transpose: <big><math>M^HM = MM^H.</math></big> |
* A [[wp:normal matrix|normal matrix]] is commutative in [[matrix multiplication|multiplication]] with its conjugate transpose: <big><math>M^HM = MM^H.</math></big> |
||
* A [[wp:unitary matrix|unitary matrix]] has its [[inverse matrix|inverse]] equal to its conjugate transpose: <big><math>M^H = M^{-1}.</math></big> <br> This is true when: <br> [[wikt:iff|'''iff''']] <math> |
* A [[wp:unitary matrix|unitary matrix]] has its [[inverse matrix|inverse]] equal to its conjugate transpose: <big><math>M^H = M^{-1}.</math></big> <br> This is true when: <br> [[wikt:iff|'''iff''']] <math>M^HM = I_n</math> and <br> [[wikt:iff|'''iff''']] <big><math>MM^H = I_n,</math></big> where <big><math>I_n</math></big> is the identity matrix. |
||