Let $f(t,y)=Ay$ for all $t \in \mathbb{R}, y \in \mathbb{R}^n$ for a symmetric Matrix $A \in \mathbb{R}^{n \times n}$. What is the smallest Lipschitz-constant for f w.r.t. y, i.e. $\|f(t,y_1)-f(t,y_2)\|_2 \le L\|y_1-y_2\|_2$ according to the eigenvalues of $A$ and is it correct that the smallest one-sided Lipschitz-constant is $\lambda_{max}$ of $\frac12 (A+A^T)$? Can someone help me?
2026-03-26 07:58:34.1774511914
Smallest Lipschitz constant for $f(t,y)=Ay$
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