Search for a tool
Complex Conjugate Matrix

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.

Results

Complex Conjugate Matrix -

Tag(s) : Matrix

Share
Share
dCode and more

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!


Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!


Feedback and suggestions are welcome so that dCode offers the best 'Complex Conjugate Matrix' tool for free! Thank you!

Complex Conjugate Matrix

Complexe Conjugate Matrix Calculator

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

Answers to Questions (FAQ)

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 "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, breaker, 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.

Cite dCode

The copy-paste of the page "Complex Conjugate Matrix" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Complex Conjugate Matrix on dCode.fr [online website], retrieved on 2024-12-04, https://www.dcode.fr/complex-conjugate-matrix

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Feedback and suggestions are welcome so that dCode offers the best 'Complex Conjugate Matrix' tool for free! Thank you!


https://www.dcode.fr/complex-conjugate-matrix
© 2024 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
 
Feedback