Titlebook: Combinatorial Matrix Theory and Generalized Inverses of Matrices; Ravindra B. Bapat,Steve J. Kirkland,Simo Puntanen Book 2013 Springer Ind

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Matrix Product of Graphs,In this paper, we characterize the graphs . and . for which the product of the adjacency matrices .(.).(.) is graphical. We continue to define matrix product of two graphs and study a few properties of the same product. Further, we consider the case of regular graphs to study the graphical property of the product of adjacency matrices.

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Inference in Error Orthogonal Models,Error Orthogonal Models constitute a very interesting class of models very useful in the design of experiments. The use of commutative Jordan algebras of symmetric matrices is used in order to perform statistical inference. The concept of segregation is introduced thus allowing the estimation of variance components.

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Sliding on Clean (Dry) Surfaces,weighted directed graph is obtained. It is a generalization of the formula for the determinant of the Laplacian matrix of a mixed graph obtained by Bapat et al. (Linear Multilinear Algebra 46:299–312, .).

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https://doi.org/10.1007/978-3-642-03448-0of writing a square matrix as a sum of idempotent matrices. Much work was done for real matrices and for matrices over other algebraic structures. We shall consider some of this work and present some new results for matrices over projective free rings.

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