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, maths, geocaching, puzzles and problems to solve every day! A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

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.

For 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 \( a-ib \) (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.

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 given 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 !