The Effect of the Additive Row Operation on the Permanent

Year 2023, Issue: 42, 8 - 13, 31.03.2023

Ahmet Zahid Küçük , Abdullah Talha Sözer

https://doi.org/10.53570/jnt.1178990

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

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