The Effect of the Additive Row Operation on the Permanent

Authors : Ahmet Zahid KÜÇÜK, Abdullah Talha SÖZER

Pages : 8-13

Doi:10.53570/jnt.1178990

View : 13 | Download : 8

Publication Date : 2023-03-31

Article Type : Research Paper

Abstract :The permanent function is not as stable as the determinant function under the elementary row operations. For example, adding a non-zero scalar multiple of a row to another row does not change the determinant of a matrix, but this operation changes its permanent. In this article, the variation in the permanent by applying the operation, which adds a scalar multiple of a row to another row, is examined. The relationship between the permanent of the matrix to which this operation is applied and the permanent of the initial matrix is given by a theorem. Finally, the paper inquires the need for further research.
Keywords : Permanent, Gaussian elimination, elementary row operations, Laplace expansion