Linear Algebra - Sebastian Pancratz

Recommendations

Info

j det A = n i=1 (−1)i+j aij det(A ij ) i det A = n j=1 (−1)i+j aij det(A ij ) det A = d(A (1) , . . . , A (n) ) = = n aij(−1) i+j−2 1 ∗ d 0 A ij i=1 n i=1 (−1) i+j aij det A ij , A ∈ Mn(F) adj A n × n (i, j) (−1) i+j det A ij (adj A)A = (det A)I A A−1 = 1 det A adj A j < k det A = n (adj A)jiaij = (adj A · A)jj. i=1 0 = det(A (1) , . . . , A (k) , . . . , A (k) , . . . , A (n) ) = n (adj A)jiaik i=1 = (adj A · A)jk. 1 A det A = 0 adj A A −1 = 1 det A det A adj A · A = I Ax = b m n A m × n b F m rank A = rank(A| b) n = rank A = rank(A| b) x = A −1 b m = n A ∈ Mn(F) Ax = b x = (x1, . . . , xn) T xi = 1 detA det A îb i = 1, . . . , n A îb A i b
x Ax = b det A îb = det(A(1) , . . . , A (i−1) , b, A (i+1) , . . . , A (n) ) = j=1 = xi det A, xi = 1 detA det Aîb i = 1, . . . , n xj det(A (1) , . . . , A (i−1) , A (j) , A (i+1) , . . . , A (n) ) A ∈ Mn(Z) det A = ±1 b ∈ Z n Ax = b Z
Page 5 and 6: F R C F • F +
Page 7 and 8: V = C C 1, i v1, . .
Page 9 and 10: U ∪ W U ⊂ W W ⊂ U
Page 11 and 12: V W F α : V → W v, v1
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 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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?