ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5545 on D5945: Complex matrix trace
Trace of conjugate transpose equals conjugate of trace
Formulation 0
Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix such that
(i) $A^*$ is a D5306: Complex matrix conjugate transpose for $A$
Then \begin{equation} \text{Trace} A^* = \overline{\text{Trace} A} \end{equation}
Subresults
R5544: Real matrix trace is preserved by transposing
Proofs
Proof 0
Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix such that
(i) $A^*$ is a D5306: Complex matrix conjugate transpose for $A$