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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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Definition of characteristic polynomial of a matrix

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Characteristic and minimal polynomialsClose match
The characteristic polynomial applied to the matrix gives the 0 matrix.Close match
Definition of characteristic equation of a matrixClose match
Definition of minimal polynomial of a matrixClose match
Definition of characteristic polynomial of a linear transformationClose match
The Cayley-Hamilton theorem for a matrix.Close match
Definition of applying a polynomial to a square matrixClose match
The minimal polynomial of a square matrix exists and is unique.Close match
The eigenvalues of a matrix are the roots/solutions of its characteristic polynomial/equation.Close match
A matrix and its transpose have the same eigenvalues/characteristic polynomial.Close match
Definition of minimal polynomial of a linear transformationClose match
Diagonalizability requires splitting and equality of geometric and algebraic multiplicitiesClose match
The eigenvalues of a polynomial of a matrix are the polynomial of the eigenvalues.Close match
Definition of matrix diagonalizationRelated
The Cayley-Hamilton theorem for a linear transformationRelated
Definition of matrix multiplication in terms of column vectorsRelated
Definition of matrix multiplicationRelated
Definition of the standard matrix for a linear transformationRelated
Definition of matrix-vector productRelated
Definition of diagonalizable matrixRelated

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