Universal scaling between the eigenvector and matrix elements in one kind of random matrices

Wei Pan, Jing Wang, Deyan Sun

Published 2019-01-30Version 1

The diagonalization of matrices may be the top priority in application of modern physics. In this letter, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling between the eigenvector and matrix elements exists. Namely, each element of the eigenvector of ground states linearly correlates with the sum of matrix elements in the corresponding row. The linear relationship implies a straightforward method to directly calculate the eigenvector of ground states for a matrix, which is widely needed in many fields.