You can conjugate transpose a matrix by using the ' operator. That is
the entry in the
i
th column and the j
th row will be
the complex conjugate of the entry in the
j
th column and the i
th row of the original matrix.
For example:
[1,2,3]*[4,5,6]'We transpose the second vector to make matrix multiplication possible. If you just want to transpose a matrix without conjugating it, you would use the .' operator. For example:
[1,2,3]*[4,5,6i].'
Note that normal transpose, that is the .' operator, is much faster and will not create a new copy of the matrix in memory. The conjugate transpose does create a new copy unfortunately. It is recommended to always use the .' operator when working with real matrices and vectors.