Linear Algebra - Sebastian Pancratz

V F F
R C α : V → V
α ∈ End(V ) α B V
[α]B i = j aij = 0 α B
V [α]B i > j aij = 0
α ∈ End(V ) λ ∈ F α
v ∈ V v = 0 α(v) = λv v λ
λ α α − λι det(α − λι) = 0
λ = 0 α
χα(t) = det(α − tι) α
n = dim V A ∈ Mn(F) χα(t) = det(A − tI)
α
A λ A χA(λ) = 0 v ∈ F n
v = 0 Av = λv
χ P −1 AP (t) = det(P −1 AP − tI)
= det P −1 det(A − tI) det P
= χA(t).
1 1
0 1 2 × 2
1, 1 I
1 C
n
V C α ∈ End(V ) α
V