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Following the exact same logic as [[Calculus/ComplexVector|vector conjugation]], a matrix can also be conjugated.

This is most important for calculating the '''Hermitian transpose''', notated as either '''''A'''^H^'' or '''''A'''^†^'' ('dagger'). This involves [[LinearAlgebra/Transposition|transposing]] and taking the complex conjugate.

Matrix Conjugation

Matrix conjugation is an evolution of vector conjugation.

Contents

  1. Matrix Conjugation
    1. Description
      1. Properties

Description

Following the exact same logic as vector conjugation, a matrix can also be conjugated.

This is most important for calculating the Hermitian transpose, notated as either AH or A† ('dagger'). This involves transposing and taking the complex conjugate.

Properties

The double conjugate of a matrix is the original matrix: double.svg

Conjugation is distributive: dist.svg

The transpose of a conjugate is equal to the conjugate of the transpose: trans.svg

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LinearAlgebra/MatrixConjugation (last edited 2026-02-13 03:19:26 by DominicRicottone)