[PDF]線形代数学まとめ３ 行列の固有値・固有ベクトル( II, 3, 2002 ) 3 1 • n × n A ∗) λ ∈ R, x ∈ Rn Ax = λx, x = \ 0 (Eq-1) λ A x λ A †) • ΦA(x) := |xIn − A| = xn + . . . A ΦA(x) xn n 1 λ A ⇐⇒ ΦA(λ) = 0. n ΦA(x) = 0 ‡) • λ (λIn − A)x = 0 (Eq-2) 0 A = 0 6 3 −2 7 2 0 0 3 ΦA(x) = |xI3 − A| = � � � � � � � � x −6 −3 2 x − 7 −2 0 0 x − 3 � � � � � � � � = . . . ( ) · · · = (x − 4)(x − 3)2 4 3 x = 3 (3I3 − A)x = 0 3I3 − A = 3 −6 −3
