Linear Algebra - Sebastian Pancratz

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Bi Vi B = k i=1 Bi Vi i Vi ∩ j=i Vj = {0} k > 2 Vi ∩ Vj = {0} i = j =⇒ Bi Vi B = k i=1 Bi v ∈ Vi v = k i=1 vi vi Bi vi v B B 0 Vi vi Vi v1 +· · ·+vk = 0 0 vi = 0 Bi 0
V W F α : V → W v, v1, v2 ∈ V λ ∈ F α(v1 + v2) = α(v1) + α(v2) α(λv) = λα(v) D : D(R) → F (R) = R R f ↦→ f t x 0 : C[0, 1] → F [0, 1] f ↦→ x 0 f(t) t A m × n α : F n → F m x ↦→ Ax U, V, W ιv : V → V, v ↦→ v U β −→ V α −→ W α, β α ◦ β : U → W V W F B V α0 : B → W α : V → W α0 α(v) = α0(v) v ∈ B v ∈ V v = λ1v1 + · · · + λnvn vi ∈ B λi ∈ F α(v) = λiα0(vi) α V W F α : V → W V W V → W F ιV : V → V α : V → W α −1 : W → V U α −→ V β −→ W β ◦ α : U → W
Page 5 and 6: F R C F • F +
Page 7 and 8: V = C C 1, i v1, . .
Page 9: U ∪ W U ⊂ W W ⊂ U
Page 13 and 14: • n i=k+1 λiα(vi) = 0 α( n i
Page 15 and 16: B = {u1, . . . , un} C = {v1, . . .
Page 17: A ∈ Mm,n(F) rowrk(A) = dim rowsp
Page 20 and 21: d d(e1, . . . , en) = 1
Page 22 and 23: A A det A = 0 A A
Page 24 and 25: j det A = n i=1 (−1)i+j aij det(
Page 27 and 28: V F F R C α : V → V
Page 29 and 30: α ∈ End(V ) U V α(U) ≤ U
Page 31 and 32: deg p p l al = 0 −∞
Page 33 and 34: α p(α) = 0 mα
Page 35: n = 4 (λ−t) 4 4 4 = 3 +
Page 38 and 39: λ ∈ F θ ∈ V ∗ = α ∗ (θ
Page 41 and 42: U, V F ψ : U × V → F
Page 43 and 44: B0 = {e1, e2, . . . , en} e1 = e
Page 45 and 46: C e1, . . . , en ψ
Page 47: ψ : U × V → F ψL : U → V
Page 50 and 51: R n C n V = C[0, 1] 〈(, f
Page 52 and 53: = 〈αw, v〉 = 〈v, αw〉 〈v
Page 54: A n × n V n B

Linear Algebra - Sebastian Pancratz

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