ON TRANSINVERSE OF MATRICES AND ITS APPLICATIONS
Publish place: Journal of Algebraic Systems، Vol: 12، Issue: 1
Publish Year: 1403
Type: Journal paper
Language: English
View: 124
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Document National Code:
JR_JAS-12-1_009
Index date: 18 July 2023
ON TRANSINVERSE OF MATRICES AND ITS APPLICATIONS abstract
Given a matrix A with elements from a field of characteristic zero, the transin-verse A# of A is defined as the transpose of the matrix obtained by replacing the non-zero elements of A by their inverses and leaving zeros, if any, unchanged.We discuss the properties of this matrix operation in some detail and as an important application, we reinvent the celebrated matrix tree theorem for gain graphs.Characterization of balance in connected gain graphs using its Laplacian matrix becomes an immediate consequence.
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ON TRANSINVERSE OF MATRICES AND ITS APPLICATIONS authors
K Shahul Hameed
Department of Mathematics, K M M Government Women’s College, Kannur, P.O. Box ۶۷۰۰۰۴, Kerala, India
K O Ramakrishnan
Department of Mathematics, K M M Government Women’s College, Kannur, P.O. Box ۶۷۰۰۰۴, Kerala, India
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