Eigenvalue, Eigenvector

GIMP (Gnu Image Manipulation Program) made me wanna know bout Eigenvalue.

Eigenvalue, Eigenvector = Characteristic value, Characteristic vector.

Eigenvalue,CharacteristicValue_IMG_1859

#characteristic_equation #det #determinant #if_and_only_if #characteristic_polynomial #cayley-hamilton_theorem

Characteristic equation = Characteristic polynomial

@Oxford consise dictionary of Mathematics

CAYLEY-HAMILTON Theorem
Characteristic polynomial p(Λ)
p(Λ)=det(A-λI)

p(λ) = (-1**n)(λ**n + bn-1*λ**n-1 + ・・・ + b1λ + b0), (bn is sequence)

A**n+bn-1A**n-1+・・・+b1A+b0I=O