Degree Growth of Matrix Inversion : Birational Maps of Symmetric , Cyclic Matrices

@inproceedings{Bedford2005DegreeGO,
  title={Degree Growth of Matrix Inversion : Birational Maps of Symmetric , Cyclic Matrices},
  author={Eric Bedford and Kyounghee Kim},
  year={2005}
}
§0. Introduction Let Mq denote the space of q×q matrices, and let P(Mq) denote its projectivization. For a matrix x = (xij) we consider two maps. One is J(x) = (x −1 ij ) which takes the reciprocal of each entry of the matrix, and the other is the matrix inverse I(x) = (xij) . The involutions I and J , and thus the mapping K = I ◦ J , arise as basic symmetries in Lattice Statistical Mechanics (see [BM], [BMV]). This leads to the problem of determining the iterated behavior of K on P(Mq) (see… CONTINUE READING

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