Given a square n x n matrix A, is it possible to find the determinant of the matrix for large values of n easily, and thereby as n goes to infinity? I know that the number of components of the determinants in creases with n!, but I want to know if there is a way around this with large matrices and I couldn't find one on wiki.
2026-04-22 07:14:29.1776842069
determinants of large and infinite matrices
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There are algorithms based on matrix decompositions that have polynomial running time in the dimension. Certainly, computing the determinant of a large matrix by hand is still a pain, but these algorithms make computing the determinant reasonably fast on a computer.
As for infinite matrices, you have to decide what the meaning of the determinant of an infinite matrix is, since the naive definition would admit infinite determinants. Part of operator theory and functional analysis is to find the right definition.