ThmDex – An index of mathematical definitions, results, and conjectures.
Derivative for an affine real matrix function
Formulation 1
Let $f : \mathbb{R}^{N \times M} \to \mathbb{R}^{K \times M}$ be a D5655: Real matrix function such that
(i) $A \in \mathbb{R}^{K \times N}$ and $B \in \mathbb{R}^{K \times M}$ are each a D4571: Real matrix
(ii) \begin{equation} f(X) = A X + B \end{equation}
Let $L : \mathbb{R}^{N \times M} \to \mathbb{R}^{K \times M}$ be a D5655: Real matrix function such that
(i) \begin{equation} L(X) = A X \end{equation}
Then $L$ is a D5787: Real matrix function derivative for $f$ on $\mathbb{R}^{N \times M}$.