Degree Complexity of Matrix Inversion
Dynamical Systems
2009-07-21 v1 Complex Variables
Abstract
For a q by q matrix x=(x_{i,j}) we let J(x)=(x_{i,j}^{-1}) be the Hadamard inverse, which takes the reciprocal of the elements of x . We let I(x)=(x_{i,j})^{-1} denote the matrix inverse, and we define K=I\circ J to be the birational map obtained from the composition of these two involutions. We consider the iterates K^n=K\circ...\circ K and determine degree complexity of K, which is the exponential rate of degree growth of the degrees of the iterates.
Keywords
Cite
@article{arxiv.0907.3319,
title = {Degree Complexity of Matrix Inversion},
author = {Eric Bedford and Tuyen Trung Truong},
journal= {arXiv preprint arXiv:0907.3319},
year = {2009}
}