Degree Complexity of Matrix Inversion

Details Degree Complexity of Matrix Inversion Degree Complexity of Matrix Inversion

2009-07-19

arxiv.org/abs/0907.3319v1

Mathematics

Dynamical Systems

Scientific paper

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.

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