ON TRANSINVERSE OF MATRICES AND ITS APPLICATIONS

Document Type : Original Manuscript

Authors

Department of Mathematics, K M M Government Women’s College, Kannur, P.O. Box 670004, Kerala, India

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.

Keywords

References

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Journal of Algebraic Systems
Volume 12, Issue 1
September 2024
Pages 135-147

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