TY - JOUR
ID - 2842
TI - ON TRANSINVERSE OF MATRICES AND ITS APPLICATIONS
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Shahul Hameed, Koombail
AU - Ramakrishnan, Kunhumbidukka Othayoth
AD - Department of Mathematics, K M M Government Womenâ€™s College, Kannur, P.O.
Box 670004, Kerala, India
Y1 - 2024
PY - 2024
VL - 12
IS - 1
SP - 135
EP - 147
KW - Gain graph
KW - Signed graph
KW - graph eigenvalues
KW - Graph Laplacian
DO - 10.22044/jas.2022.12107.1629
N2 - 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.
UR - https://jas.shahroodut.ac.ir/article_2842.html
L1 - https://jas.shahroodut.ac.ir/article_2842_63f0c500dfc9cf0ede99189cacc5ba3a.pdf
ER -