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Characteristic and minimal polynomials
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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 minimal polynomial of a square matrix exists and is unique.
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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The eigenvalues of a matrix are the roots/solutions of its characteristic polynomial/equation.
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Characteristic and minimal polynomials