Search for a tool
Conjugate Transpose Matrix

Tool to calculate the conjugate transpose matrix (or Hermitian transpose matrix), the transpose of the conjugate matrix of a complex 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!


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

Conjugate Transpose Matrix

Conjugate Transpose Matrix Calculator

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

Hermitian Matrix Checker

Calculate the Conjugate Transpose matrix if it is equal to the initial matrix then the matrix is Hermitian.

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)

Taking $ M=[a_{ij}] $ 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: $$ M=\begin{bmatrix} 2 & 1-i & 0 \\ 1 & 2+i & -i \end{bmatrix} \Rightarrow M^*= \begin{bmatrix} 2 & 1 \\ 1+i & 2-i \\ 0 & i \end{bmatrix} $$

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 "Conjugate Transpose Matrix" source code. Except explicit open source licence (indicated Creative Commons / free), the "Conjugate Transpose Matrix" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, 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, or API access for "Conjugate Transpose 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 "Conjugate Transpose 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):
Conjugate Transpose Matrix on dCode.fr [online website], retrieved on 2024-06-18, https://www.dcode.fr/conjugate-transpose-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 'Conjugate Transpose Matrix' tool for free! Thank you!


https://www.dcode.fr/conjugate-transpose-matrix
© 2024 dCode — El 'kit de herramientas' definitivo para resolver todos los juegos/acertijos/geocaching/CTF.
 
Feedback