Linear mapping/Trigonalizable/Characterizations/1/Fact

< Linear mapping < Trigonalizable < Characterizations < 1
Characterization of trigonalizable mappings

Let denote a field, and let denote a finite-dimensional vector space. Let

denote a linear mapping. Then the following statements are equivalent.

  1. is trigonalizable.
  2. There exists a -invariant flag.
  3. The characteristic polynomial splits into linear factors.
  4. The minimal polynomial splits into linear factors.
Proof, Write another proof
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