ConjugateTranspose

ConjugateTranspose[m]

or gives the conjugate transpose of .

Details and Options

Examples

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Basic Examples  (2)

Conjugate transpose of a complex-valued matrix:

Enter using ct:

Scope  (2)

Conjugate transpose a sparse array:

The conjugate transpose is sparse:

ConjugateTranspose works for symbolic matrices:

ComplexExpand assumes all variables are real:

Generalizations & Extensions  (1)

ConjugateTranspose works similarly to Transpose for tensors:

Conjugate and transpose the first two dimensions:

Conjugate and transpose the first and third dimensions:

Applications  (1)

is a random complex matrix:

Find the QRDecomposition of :

is unitary, so its inverse is

Reconstruct from the decomposition:

Properties & Relations  (2)

ConjugateTranspose[m] is equivalent to Conjugate[Transpose[m]]:

The product of a matrix and its conjugate transpose is Hermitian:

is the matrix product of and :

so is Hermitian:

Wolfram Research (2004), ConjugateTranspose, Wolfram Language function, https://reference.wolfram.com/language/ref/ConjugateTranspose.html.

Text

Wolfram Research (2004), ConjugateTranspose, Wolfram Language function, https://reference.wolfram.com/language/ref/ConjugateTranspose.html.

BibTeX

@misc{reference.wolfram_2020_conjugatetranspose, author="Wolfram Research", title="{ConjugateTranspose}", year="2004", howpublished="\url{https://reference.wolfram.com/language/ref/ConjugateTranspose.html}", note=[Accessed: 18-January-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_conjugatetranspose, organization={Wolfram Research}, title={ConjugateTranspose}, year={2004}, url={https://reference.wolfram.com/language/ref/ConjugateTranspose.html}, note=[Accessed: 18-January-2021 ]}

CMS

Wolfram Language. 2004. "ConjugateTranspose." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ConjugateTranspose.html.

APA

Wolfram Language. (2004). ConjugateTranspose. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ConjugateTranspose.html