Dashboard

Featured nodes

Roots

Public root

Templates

Guanyu's Latex template
Router template

Trees

Showcase

Related nodes

Parents1

Characteristic and minimal polynomials

Siblings8
Sort by title
Sort by date

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.

Beta

#

Explore
Sign in
Request an invite

The eigenvalues of a matrix are the roots/solutions of its characteristic polynomial/equation.

Related

Your own links and the nodes closest in meaning.

Related

Sign in to manage links and suggestions.

Similar in meaning

Suggested from content

MultiplicityClose match
Every matrix has an eigenvalue over the complex numbers.Close match
Definition of eigenvalue of a matrixClose match
The eigenvalues of a polynomial of a matrix are the polynomial of the eigenvalues.Close match
Definition of characteristic equation of a matrixClose match
The eigenvalues of a scalar multiple of a matrix are the scalar multiples of the eigenvalues.Close match
Definition of eigenvalue/characteristic value of a linear transformationClose match
An eigenspace of a matrix is a nontrivial subspace.Close match
Definition of (algebraic) multiplicity of an eigenvalueClose match
Characteristic and minimal polynomialsClose match
The dimension of a eigenspace is less than or equal to the (algebraic) multiplicity of the eigenvalue.Close match
A matrix with real entries has eigenvalues occurring in conjugate pairs.Close match
Every nonzero finite-dimensional complex operator has an eigenvalueClose match
The eigenvalues of a power of a matrix are the power the eigenvalues.Close match
A matrix and its transpose have the same eigenvalues/characteristic polynomial.Close match
Definition of eigenvector/characteristic vector of a linear transformationClose match
Definition of characteristic polynomial of a matrixClose match
The eigenvalues of the inverse of a nonsingular matrix are the reciprocals of the eigenvalues.Close match
Definition of eigenspace of a matrixClose match
Definition of characteristic polynomial of a linear transformationClose match

knowen.md© 2026 KTree Inc.

Explore What is knowen.md?Pricing Integrations Contact us Leave feedback