When doing the [[Matrix Transpose|Matrix Transpose]] of a [[Matrix|Matrix]] with [[Complex Numbers|Complex]] values, it makes more sense to use the [[Transpose Conjugate]]. $\huge \vec v^{*} $ The [[Transpose Conjugate]] of any matrix is equal to the [[Matrix Transpose|Transpose]] of the [[Matrix]] with each element transforming to its [[Complex Conjugate]]. $\huge \begin{align} \vec v ^{*} &= \mat{ v_{1}^* \\ \vdots\\ v_{n}^* }^{\intercal}\\ &= \mat{ v_{1}^* & \dots& v_{n}^* } \end{align} $