Least change in the Determinant or Permanent of a matrix under perturbation of a single element: continuous and discrete cases

Details Least change in the Determinant or Permanent of a matrix under perturbation of a single element: continuous and discrete cases Least change in the Determinant or Permanent of a matrix under perturbation of a single element: continuous and discrete cases

2008-05-14

arxiv.org/abs/0805.2081v1

Computer Science

Discrete Mathematics

15 pages, 1 figure

Scientific paper

We formulate the problem of finding the probability that the determinant of a matrix undergoes the least change upon perturbation of one of its elements, provided that most or all of the elements of the matrix are chosen at random and that the randomly chosen elements have a fixed probability of being non-zero. Also, we show that the procedure for finding the probability that the determinant undergoes the least change depends on whether the random variables for the matrix elements are continuous or discrete.

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