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} $ 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:

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 online 'Complex Conjugate Matrix' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Complex Conjugate Matrix download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!