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.

Complex Conjugate Matrix - dCode

Tag(s) : Matrix

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*!

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)

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.

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

dCode retains ownership of the "Complex Conjugate Matrix" source code. Except explicit open source licence (indicated Creative Commons / free), the "Complex Conjugate Matrix" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Complex Conjugate Matrix" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Complex Conjugate Matrix" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Complex Conjugate Matrix" or any of its results, is allowed as long as you cite dCode!

Cite as source (bibliography):

*Complex Conjugate Matrix* on dCode.fr [online website], retrieved on 2022-11-28,

conjugate,complex,matrix,i,bar

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

© 2022 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback