ON TRANSINVERSE OF MATRICES AND ITS APPLICATIONS
نویسندگان
1 Department of Mathematics, K M M Government Women’s College, Kannur, P.O. Box 670004, Kerala, India
2 Department of Mathematics, K M M Government Women’s College, Kannur, P.O. Box 670004, Kerala, India
doi
10.22044/jas.2022.12107.1629چکیده
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.
