OAI/GroupTheory/PolycyclicRecognition/Algebra/PolynomialMatrixGenericPosition.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

Simultaneous generic position in an irreducible polynomial matrix group

A finite collection of proper linear subspaces can be avoided both by a matrix and its inverse whenever each vector has a spanning orbit.

  1. theorem OAI.PolycyclicRecognition.finite_open_intersection_nonempty line 15
  2. theorem OAI.PolycyclicRecognition.PolynomialMatrixGroup.exists_simultaneous_forward_inverse_avoidance line 38