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

Conjugate Transpose Matrix - dCode

Tag(s) : Mathematics, Algebra, Symbolic Computation

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

This page is using the new English version of dCode, *please make comments* !

Sponsored ads

This script has been updated, please report any problems.

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

The conjugate transpose matrix is calculated for a matrix with complex elements. This is the transposed matrix of the conjugate matrix (or the conjugate matrix of the transposed matrix).

Consider \( M=[a_{ij}] \) a matrix, the conjugate transpose matrix is noted \( M^*=\overline{M}^T=\overline{M^T}=[\overline{a_{ij}}]^T \) (There is also a notation with a dagger †).

$$ M=\begin{pmatrix} 2 & 1-i & 0 \\ 1 & 2+i & -i \end{pmatrix} \Rightarrow M^*= \begin{pmatrix} 2 & 1 \\ 1+i & 2-i \\ 0 & i \end{pmatrix} $$

On dCode, use the character i to represent the imaginary unit \( i \) of complex numbers.

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.

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

dCode retains ownership of the source code of the script Conjugate Transpose Matrix. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Conjugate Transpose Matrix script for offline use, for you, your company or association, see you on contact page !

conjugate,transpose,complex,matrix,i

Source : http://www.dcode.fr/conjugate-transpose-matrix

© 2017 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode