# Hermitian

Hermitian[{1,2}]

represents the symmetry of a Hermitian matrix.

# Details

• A Hermitian matrix is also known as a self-adjoint matrix.
• A square matrix m is Hermitian if ConjugateTranspose[m]m.

# Examples

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## Basic Examples(2)

This matrix is Hermitian:

Find conditions for which a matrix is Hermitian:

## Scope(2)

Use Hermitian[] as a symmetry for matrix domains:

Use the specification to simplify symbolic matrix expressions:

Symmetrize matrices with respect to Hermitian symmetry:

## Applications(2)

Take a 3×3 matrix of complexes:

It is not a Hermitian matrix:

Compute its Hermitian part:

Find the Hermitian matrix with minimum 2-norm (largest singular value) such that the matrix is positive semidefinite:

## Properties & Relations(2)

Hermitian[slots] for an array of real entries automatically converts into Symmetric[slots]:

The diagonal elements of a Hermitian matrix are real:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2022_hermitian, author="Wolfram Research", title="{Hermitian}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/Hermitian.html}", note=[Accessed: 29-November-2022 ]}

#### BibLaTeX

@online{reference.wolfram_2022_hermitian, organization={Wolfram Research}, title={Hermitian}, year={2020}, url={https://reference.wolfram.com/language/ref/Hermitian.html}, note=[Accessed: 29-November-2022 ]}