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  • Characteristic and minimal polynomials

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  • The minimal polynomial of a square matrix exists and is unique.
  • Definition of applying a polynomial to a square matrix
  • Definition of characteristic polynomial of a matrix
  • Definition of characteristic equation of a matrix
  • Definition of minimal polynomial of a matrix
  • The eigenvalues of a matrix are the roots/solutions of its characteristic polynomial/equation.
  • The characteristic polynomial applied to the matrix gives the 0 matrix.
  • The Cayley-Hamilton theorem for a matrix.
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  1. Definition of applying a polynomial to a square matrix

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  • Axioms of a vector space#23798
  • Bases#23828
  • Basic properties#23957
  • Basic properties of linear transformations#23863
  • Basic terminology#23412
  • Basic terminology and notation#23448
  • Basis exchange using a nonzero coordinate#23990
  • Block matrices#23567
  • Canonical forms of matrices#23608
  • Change of coordinates matrices are invertible#23998
  • Characteristic and minimal polynomials#23699
  • Choosing factorizations and understanding numerical error#37115
  • C^n is a vector space.#24098
  • Cofactors#23716
  • Commuting diagonalizable and nilpotent decomposition over the complex numbers#23585
  • Complex inner products conjugate scalars in the first argument#23900
  • Composition#24022
  • Condition number measures relative sensitivity#23750
  • Conjugating by a change of coordinates matrix converts matrix representations with respect to different bases.#23999
  • Conjugation#23464
  • Container for Linear Algebra#24123
  • Coordinates#23989
  • Coordinate vector spaces#23776
  • Cramer's rule#23722
  • Definition and terminology#23954
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  • Aspen Summer 2016 - Entanglement Matters#1213
  • Container for Linear Algebra#24123
  • Math#23168
  • Test Flight Problem Set#23151

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