利用Hilbert度量的复扩张证明Hopf不等式
A New Proof of Hopf's Inequality Using a Complex Extension of the Hilbert Metric
摘要：
由Perron-Frobenius理论可知，正方阵的谱隙为正。在本文中，我们给出了一个更定量的表征的光谱间隙。更具体地说，使用一个复杂的扩展的希尔伯特度量，我们表明，所谓的频谱比的正方阵的Birkhoff收缩系数的上限，这反过来又产生一个下界的频谱间隙。
英文摘要：
It is well known from the Perron-Frobenius theory that the spectral gap of a positive square matrix is positive. In this paper, we give a more quantitative characterization of the spectral gap. More specifically, using a complex extension of the Hilbert metric, we show that the so-called spectral ratio of a positive square matrix is upper bounded by its Birkhoff contraction coefficient, which in turn yields a lower bound on its spectral gap.
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