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.
Categories: math.DS math.CV