Search for a tool
Conjugate Transpose Matrix

Tool to calculate adjoint matrix (or Hermitian transpose). The adjoint matrix is the transpose of the conjugate matrix of a matrix M.

Results

Conjugate Transpose 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!


Thanks to your feedback and relevant comments, dCode has developed the best 'Conjugate Transpose Matrix' tool, so feel free to write! Thank you!

Conjugate Transpose Matrix

Conjugate Transpose Matrix Calculator

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

Answers to Questions (FAQ)

What is a matrix conjugate transpose? (Definition)

The conjugate transpose matrix is the name given to the transpose of the conjugate of a complex matrix (or of the conjugate of the transposed matrix), it is denoted $ M^* $ (asterisk) or, more rare notation, with a dagger † $ M^\dagger $.

How to calculate the conjugate transpose of a matrix? (Formula)

$ M=[a_{ij}] $ is a matrix with complex elements, the conjugate transpose matrix is computed with the formula $$ M^* = \overline{M}^T = \overline{M^T} = [\overline{a_{ij}}]^T $$

Example: The conjugate transpose 2x2 matrix $ M^* $ of the matrix $ M $ is calculated: $$ M=\begin{pmatrix} 2 & 1-i & 0 \\ 1 & 2+i & -i \end{pmatrix} \Rightarrow M^*= \begin{pmatrix} 2 & 1 \\ 1+i & 2-i \\ 0 & i \end{pmatrix} $$

On dCode, use the character i to represent the imaginary unit $ i $ of complex numbers.

What is the hermitian transpose?

Hermitian transpose is another name of the conjugate transpose matrix, mainly used on linear function spaces. Other names used : Hermitian conjugate, bedaggered matrix or transjugate.

What is the adjoint matrix?

In English, the conjugate transposed matrix is sometimes erroneously called adjoint matrix but it is not the same matrix.

Source code

dCode retains ownership of the online "Conjugate Transpose Matrix" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Conjugate Transpose Matrix" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Conjugate Transpose 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, copy-paste, or API access for "Conjugate Transpose Matrix" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

Need Help ?

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

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Conjugate Transpose Matrix' tool, so feel free to write! Thank you!


Source : https://www.dcode.fr/conjugate-transpose-matrix
© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback