## Conjugate Transpose and Transpose Operator

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.