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

Result R5174 on D398: Matrix transpose

Transpose of a product of two complex matrices

Formulation 0

Let $A \in \mathbb{C}^{N \times M}$ and $B \in \mathbb{C}^{M \times K}$ each be a D999: Complex matrix.

Then \begin{equation} (A B)^T = B^T A^T \end{equation}

Proofs

Proof 0

Let $A \in \mathbb{C}^{N \times M}$ and $B \in \mathbb{C}^{M \times K}$ each be a D999: Complex matrix.

This result is a particular case of R4668: Transpose of a finite product of complex matrices. $\square$