ThmDex – An index of mathematical definitions, results, and conjectures.
Transpose of a product of three complex matrices
Formulation 0
Let $A \in \mathbb{C}^{N \times M}$, $B \in \mathbb{C}^{M \times K}$, and $C \in \mathbb{C}^{K \times H}$ each be a D999: Complex matrix.
Then \begin{equation} (A B C)^T = C^T B^T A^T \end{equation}
Proofs
Proof 0
Let $A \in \mathbb{C}^{N \times M}$, $B \in \mathbb{C}^{M \times K}$, and $C \in \mathbb{C}^{K \times H}$ each be a D999: Complex matrix.
This result is a particular case of R4668: Transpose of a finite product of complex matrices. $\square$