This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# ConjugateTranspose

 ConjugateTranspose[m]or gives the conjugate transpose of .
• can be entered as Esc ct Esc or \[ConjugateTranspose].
• ConjugateTranspose[m] can also be given as , where can be entered as Esc hc Esc or \[HermitianConjugate].
Conjugate transpose of a complex-valued matrix:
Enter using Esc ct Esc:
Conjugate transpose of a complex-valued matrix:
 Out[2]//MatrixForm=
 Out[3]//MatrixForm=

Enter using Esc ct Esc:
 Out[1]=
 Scope   (2)
Conjugate transpose a sparse array:
The conjugate transpose is sparse:
ConjugateTranspose works for symbolic matrices:
ComplexExpand assumes all variables are real:
ConjugateTranspose works similarly to Transpose for tensors:
Conjugate and transpose the first two dimensions:
Conjugate and transpose the first and third dimensions:
 Applications   (1)
is a random complex matrix:
Find the QRDecomposition of :
is unitary, so its inverse is
Reconstruct from the decomposition:
ConjugateTranspose[m] is equivalent to Conjugate[Transpose[m]]:
The product of a matrix and its conjugate transpose is Hermitian:
is the matrix product of and .
so is Hermitian:
New in 5.1