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Titlebook: Combinatorial Matrix Theory; Richard A. Brualdi,Ángeles Carmona,Dragan Stevanov Textbook 2018 Springer International Publishing AG, part o

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https://doi.org/10.1007/978-3-319-70953-6permutation matrices; tournament matrices; sign pattern matrices; generalized inverses; adjacency; laplac
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978-3-319-70952-9Springer International Publishing AG, part of Springer Nature 2018
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The Group Inverse of the Laplacian Matrix of a Graph,es. The presentation below draws heavily from Kirkland–Neumann [11, Ch. 7], and the interested reader can find further results on the topic in that book. We note that Molitierno [13] also covers some of the material presented in this chapter, and so serves as another source for readers interested in pursuing this subject further.
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Daniel Alpay,Fabrizio Colombo,Irene Sabadinition as a permutation matrix, this partial order is related to Gaussian elimination and leads to the matrix Bruhat decomposition of a nonsingular matrix, and then to a characterization of ags in a vector space. We also describe a correspondence between permutations that are involutions (symmetric pe
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https://doi.org/10.1007/978-3-211-85782-3es. The presentation below draws heavily from Kirkland–Neumann [11, Ch. 7], and the interested reader can find further results on the topic in that book. We note that Molitierno [13] also covers some of the material presented in this chapter, and so serves as another source for readers interested in
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https://doi.org/10.1007/978-3-211-85782-3h differs from others because the tools we use come from discrete potential theory, in which we have been working for a long period, trying to emulate as much as possible the continuous case. This chapter introduces this way of approximating a problem typical of matrix theory and offers an overview
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2297-0304 delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem..978-3-319-70952-9978-3-319-70953-6Series ISSN 2297-0304 Series E-ISSN 2297-0312
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