Define $F: \mathbb{R}^{m\times n} \to \mathbb{R}^{p\times q} $,assuming F is differentiable，What is the general solution for the lipschitz constant L that satisfies $\| F(B)-F(A) \| \leq L \|B-A\|$? $\|\cdot\|$ is induced matrix norm . Is it also related to partial derivatives ((i.e. $\| \frac{ \partial vec(F(X))}{\partial (vecX)^T} \|$ ) like Jacobian matrix to vector-valued function?
2026-03-27 03:57:27.1774583847
The General Solution of Lipschitz Constant for Matrix-Valued Matrix Function
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