Linear Algebra - Sebastian Pancratz

λv = 0 λ = 0 λ −1 λ −1 (λv) = λ −1 0 = 0
λ −1 (λv) = (λ −1 λ)v = 1v = v v = 0
F n n F
X F X X → F F
V F U ⊂ V V
U ≤ V
• 0 ∈ U
• u1, u2 ∈ U =⇒ u1 + u2 ∈ U
• λ ∈ F, u ∈ U =⇒ λu ∈ U
U = ∅ U
V F U ≤ V U F
+ · V U
R R R C(R)
D(R) P (R)
n ∈ N0 λ1, . . . , λn ∈ F v1, . . . , vn ∈ V n
i=1 λivi
λ1v1 + · · · + λnvn 0
i=1 λivi = 0
S ⊂ V
v∈S λvv
v λv = 0
v1, . . . , vn V V F v ∈ V
v1, . . . , vn V = 〈v1, . . . , vn〉
S ⊂ V S V
∀v ∈ V ∃n ∈ N0 ∃v1, . . . , vn ∈ V ∃λ1, . . . , λn ∈ F v =
P2(R) 1, x, x 2
P (R)
n
λivi.
v1, . . . , vn V F
λ1v1 + · · · λnvn = 0 λ1 = · · · = λn = 0
S ⊂ V S
S
0 1 · 0 = 0
V = C R 1, i
i=1