On the properties of Laplacian pseudoinverses
On the properties of Laplacian pseudoinverses
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关于拉普拉斯伪逆的性质
DOI：
10.1109/cdc45484.2021.9683525
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
C. Altafini
中科院分区：
文献类型：
--
作者：
Angela Fontan;C. Altafini
图形laplacian的伪源用于许多应用和领域，例如在计算电网络中有效阻力的计算中，计算Markov链的击球/通勤时间和连续时间分布式的平均问题。在本文中，我们表明Laplacian伪源通常不是Laplacian矩阵，而是签名的Laplacian，其特性是最终是指数为正的矩阵，即服从强大的Perron-frobenius属性。我们进一步表明，与基质伪插入相对于这种结构（即最终指数阳性）的一组签名的拉普拉斯人（即最终指数阳性）是封闭的。即使对于签名的挖掘机，也是如此，前提是我们限制了体重平衡的拉普拉斯人也可以保证稳定性。
The pseudoinverse of a graph Laplacian is used in many applications and fields, such as for instance in the computation of the effective resistance in electrical networks, in the calculation of the hitting/commuting times for a Markov chain and in continuous-time distributed averaging problems. In this paper we show that the Laplacian pseudoinverse is in general not a Laplacian matrix but rather a signed Laplacian with the property of being an eventually exponentially positive matrix, i.e., of obeying a strong Perron-Frobenius property. We show further that the set of signed Laplacians with this structure (i.e., eventual exponential positivity) is closed with respect to matrix pseudoinversion. This is true even for signed digraphs, and provided that we restrict to Laplacians that are weight balanced also stability is guaranteed.
影响因子：
6.8
作者：
Wei Chen;Dan Wang;Ji Liu;Yongxin Chen;Sei Zhen Khong;T. Başar;K. Johansson;L. Qiu
通讯作者：
Wei Chen;Dan Wang;Ji Liu;Yongxin Chen;Sei Zhen Khong;T. Başar;K. Johansson;L. Qiu