Ela a Note on Block Representations of the Group Inverse of Laplacian Matrices
نویسندگان
چکیده
Let G be a weighted graph with Laplacian matrix L and signless Laplacian matrix Q. In this note, block representations for the group inverse of L and Q are given. The resistance distance in a graph can be obtained from the block representation of the group inverse of L.
منابع مشابه
Generalized Drazin inverse of certain block matrices in Banach algebras
Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.
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REPRESENTATIONS FOR THE DRAZIN INVERSE OF BLOCK CYCLIC MATRICES M. CATRAL AND P. VAN DEN DRIESSCHE Abstract. A formula for the Drazin inverse of a block k-cyclic (k ≥ 2) matrix A with nonzeros only in blocks Ai,i+1, for i = 1, . . . , k (mod k) is presented in terms of the Drazin inverse of a smaller order product of the nonzero blocks of A, namely Bi = Ai,i+1 · · ·Ai−1,i for some i. Bounds on ...
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Suppose R is a Bezout domain. In this paper, some necessary and sufficient conditions for the existence of the group inverse for square matrix over R are given, the conditions for the existence of the group inverse of products of matrices are studied, and the equivalent conditions for reverse order law of group inverse of product of matrices are obtained. Also the existence and the representati...
متن کاملA note on the representation for the Drazin inverse of 2× 2 block matrices
In this note the representations of the Drazin inverse of a 2×2 block matrix M = [ A B C D ] , where A and D are square matrices, have been recently developed under some assumptions. We derive formulae for the Drazin inverse of a block matrix M under conditions weaker than those in the papers [9], [11], [12] and [14]. 2000 Mathematics Subject Classification: 15A09
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