ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5544 on D5946: Real matrix trace
Real matrix trace is preserved by transposing
Formulation 0
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that
(i) $A^T$ is a D5841: Real matrix transpose for $A$
Then \begin{equation} \text{Trace} A^T = \text{Trace} A \end{equation}
Proofs
Proof 0
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that
(i) $A^T$ is a D5841: Real matrix transpose for $A$
Clear. $\square$