OAI/GroupTheory/PolycyclicRecognition/Algebra/SemisimpleSpectralOperator.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Scalar functional calculus on the eigenspaces of a semisimple operator

Only the finite-dimensional application needed for a matrix logarithm is used. The operator is constructed from the internal eigenspace direct sum.

  1. def OAI.PolycyclicRecognition.semisimpleEigenspaceEquiv line 18
  2. def OAI.PolycyclicRecognition.semisimpleSpectralOperator line 25
  3. theorem OAI.PolycyclicRecognition.semisimpleSpectralOperator_apply line 31
  4. theorem OAI.PolycyclicRecognition.semisimple_eigenspace_ext line 44
  5. theorem OAI.PolycyclicRecognition.semisimpleSpectralOperator_mul line 55
  6. theorem OAI.PolycyclicRecognition.semisimpleSpectralOperator_commute line 66