〜 ★ dCode presents ★ 〜

# Complex Conjugate Matrix

Results
Tool to calculate the complex conjugate matrix. The complex conjugate of a matrix M is a matrix denoted $\overline{M}$ composed of the complex conjugate values of each element.
Summary

## Complexe Conjugate Matrix Calculator

Loading...
(if this message do not disappear, try to refresh this page)

## Answers to Questions

### What is a complex matrix conjugate? (Definition)

The definition of a complex conjugate matrix is a matrix made of the conjugate elements of the matrix.

For the matrix $M=[a_{ij}]$, the conjugate matrix is noted with a bar $\overline{M}$ or with an asterisk $M^{*}$. For a complex value $z$, its conjugated value is written $\overline{z}$ or $z^{*}$. By generalizing, the formula for calculating the conjugate matrix is:

$$\overline{M} = [\overline{a_{ij}}] = [a_{ij}^{*}]$$

Remainder : the conjugate value of $a+ib$ is $a-ib$ (See the dCode page dedicated to complex conjugates)

### How to calculate the complex conjugate of a matrix?

The conjugate matrix is calculated for a matrix with complex elements by calculating the conjugate value of each element.

Example: $$M=\begin{bmatrix} 1 & 2-i \\ 3 & 4+2i \end{bmatrix} \Rightarrow \overline{M}= \begin{bmatrix} 1 & 2+i \\ 3 & 4-2i \end{bmatrix}$$

Use the character i to represent $i$ the imaginary unit for complex numbers.

### What are the properties of a conjugate matrix?

A double conjugated matrix (conjugated two times) is equal to the original matrix. $$\overline{\overline{M}}=M$$

## Source code

dCode retains ownership of the source code of the script Complex Conjugate Matrix online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Complex Conjugate Matrix script for offline use on PC, iPhone or Android, ask for price quote on contact page !

## Questions / Comments

Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Complex Conjugate Matrix tool. Thank you.

Source : https://www.dcode.fr/complex-conjugate-matrix
Feedback