ThmDex – An index of mathematical definitions, results, and conjectures.

Result R5554 on D5946: Real matrix trace

Real matrix trace is commutation invariant for two real matrices

Formulation 0

Let $A, B \in \mathbb{R}^{N \times M}$ each be a D4571: Real matrix.

Then \begin{equation} \text{Trace}(A B) = \text{Trace} (B A) \end{equation}

Proofs

Proof 0

Let $A, B \in \mathbb{R}^{N \times M}$ each be a D4571: Real matrix.