public class CharacteristicPolynomial extends Object implements Spectrum
p(λ) = det(A - λI)The zeros of this polynomial are the eigenvalues of A. That is, λ being an eigenvalue of A is equivalent to stating that the system of linear equations
(A - λI) v = 0where I is an identity matrix, has a non-zero solution v (namely an eigenvector). The Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic polynomial, that is, p(A) = 0 .
Constructor and Description |
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CharacteristicPolynomial(Matrix A)
Construct the characteristic polynomial for a square matrix.
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Modifier and Type | Method and Description |
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Polynomial |
getCharacteristicPolynomial()
Get the characteristic polynomial.
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List<Number> |
getEigenvalues()
Get all the eigenvalues.
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String |
toString() |
public CharacteristicPolynomial(Matrix A)
A
- a square matrixIllegalArgumentException
- if A is not squarepublic Polynomial getCharacteristicPolynomial()
public List<Number> getEigenvalues()
Spectrum
getEigenvalues
in interface Spectrum
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