Conjugate Transpose and Transpose Operator

You can conjugate transpose a matrix by using the ' operator. That is the entry in the ith column and the jth row will be the complex conjugate of the entry in the jth column and the ith row of the original matrix. For example:


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:


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.