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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.

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Conjugate Transpose Matrix -

Tag(s) : Mathematics,Algebra,Symbolic Computation

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Conjugate Transpose Matrix

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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.

Answers to Questions

How to calculate the conjugate transpose of a matrix?

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 $$M^*=\overline{M}^T=\overline{M^T}=[\overline{a_{ij}}]^T$$.

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

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 called adjoint matrix but it is not the same as the generally defined adjoint matrix.

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