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

dCode and you

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!

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Conjugate Transpose Matrix tool. Thank you.

Conjugate Transpose Matrix

Conjugate Transpose Matrix Calculator

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

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 $$M^*$$ 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.

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