R. Skip Garibaldi: The characteristic polynomial and determinant are not ad hoc constructions


Submission: 2002, Apr 11

The typical definition of the characteristic polynomial seems totally ad hoc to me. This note gives a canonical construction of the characteristic polynomial as the minimal polynomial of a ``generic'' matrix. This approach (which dates back to the late 1800s) works not just for matrices but also for a very broad class of algebras including the quaternions, all central simple algebras, and Jordan algebras. This note is intended for a broad audience.

2000 Mathematics Subject Classification: 15Axx

Keywords and Phrases: characteristic polynomial, determinant, generic minimal polynomial

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