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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Sliding Mode Control and ObservationWe discuss the regularity of matrices over .. We obtain equivalent conditions for the existence of various generalized inverses of an incline matrix. We provide an algorithm for the regularity of matrices over . and illustrate with suitable examples.

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Determinant of the Laplacian Matrix of a Weighted Directed Graph,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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,Moore–Penrose Inverse of Perturbed Operators on Hilbert Spaces,ained. The results are generalized to obtain the Moore–Penrose inverse of operators of the form .. Applications to nonnegativity of the Moore–Penrose inverse and operator partial orders are considered.

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