# 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 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_2023_antihermitian, author="Wolfram Research", title="{Antihermitian}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/Antihermitian.html}", note=[Accessed: 01-March-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2023_antihermitian, organization={Wolfram Research}, title={Antihermitian}, year={2020}, url={https://reference.wolfram.com/language/ref/Antihermitian.html}, note=[Accessed: 01-March-2024 ]}