AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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Let $A\in\mathbb{C}^{n\times n}$ be positive definite Hermitian, where $n\ge 2$, and define $\|X\|_A^2=\mathrm{tr}(AX^*X)$ for all $X\in\mathbb{C}^{n\times n}$. We determine the smallest constant $C_A$ for which $$ \|XY-YX\|_{\mathrm{F}}^2 \le C_A\|X\|_A^2\|Y\|_A^2 $$ holds for all rank-one $X,Y\in\mathbb{C}^{n\times n...
We study extremal absolute central moments of Gaussian quadratic forms under a fixed Frobenius norm. For a nonzero real symmetric matrix $M$ and $G\sim N(0,I_n)$, we construct an explicit centered difference of Gamma variables with the same mean, variance, and third centered moment as $G^{\mathsf T}MG-\operatorname{tr}...
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