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.

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day! You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

This page is using the new English version of dCode, please make comments !

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.

Answers to Questions

How to calculate the complex conjugate of a matrix?

The conjugate matrix is calculated for a matrix with complex elements. The definition of a complex conjugate matrix is simply the matrix of the conjugate elements of the matrix.

Consider the matrix \( M=[a_{ij}] \), the conjugate matrix is noted with a bar \( \overline{M} \). For a complex value \( z \), you note \( \overline{z} \) its conjugated value. Thus, the general formula is:

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

Remainder : the conjugate value of \( a+ib \) is \( a-ib \)

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. $$ \overline{\overline{M}}=M $$

Ask a new question

Source code

dCode retains ownership of the source code of the script Complex Conjugate Matrix. Except explicit open source licence (free / freeware), any algorithm, applet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any snippet or function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in PHP (or Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Complex Conjugate Matrix script for offline use, for you, your company or association, see you on contact page !

dCode uses cookies to customize the site content, analyze user behavior and adapt dCode to your use. Some data is stored and collected for advertising purposes and may be shared with our partners. OK