Antihermitian

Antihermitian[{1,2}]

represents the symmetry of an antihermitian matrix.

Details

  • An antihermitian matrix is also known as a skew-Hermitian matrix.
  • A square matrix m is antihermitian if ConjugateTranspose[m]-m.

Examples

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Basic Examples  (2)

This matrix is antihermitian:

Find conditions for which a matrix is antihermitian:

Scope  (2)

Use Antihermitian[] as a symmetry for matrix domains:

Use the specification to simplify symbolic matrix expressions:

Symmetrize matrices with respect to antihermitian symmetry:

Applications  (1)

Take a 3×3 matrix of complexes:

It is not an antihermitian matrix:

Compute its antihermitian part:

Properties & Relations  (2)

Antihermitian[slots] for an array of real entries automatically converts into Antisymmetric[slots]:

The diagonal elements of an antihermitian matrix are pure imaginary:

Wolfram Research (2020), Antihermitian, Wolfram Language function, https://reference.wolfram.com/language/ref/Antihermitian.html.

Text

Wolfram Research (2020), Antihermitian, Wolfram Language function, https://reference.wolfram.com/language/ref/Antihermitian.html.

CMS

Wolfram Language. 2020. "Antihermitian." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Antihermitian.html.

APA

Wolfram Language. (2020). Antihermitian. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Antihermitian.html

BibTeX

@misc{reference.wolfram_2022_antihermitian, author="Wolfram Research", title="{Antihermitian}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/Antihermitian.html}", note=[Accessed: 01-December-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_antihermitian, organization={Wolfram Research}, title={Antihermitian}, year={2020}, url={https://reference.wolfram.com/language/ref/Antihermitian.html}, note=[Accessed: 01-December-2022 ]}