Capítulo 0 Álgebra vetorial - Instituto de Matemática - UFRGS
Capítulo 0 Álgebra vetorial - Instituto de Matemática - UFRGS Capítulo 0 Álgebra vetorial - Instituto de Matemática - UFRGS
0 0 u − v = u + (−1) · v. (−1) · v −v v + (−v) = v + (−1)v = (1 − 1)v = 0v = 0. α · v αv {v1, v2, . . . , vn} {α1, α2, . . . , αn} αi = 0 n αivi = 0 i=1 {v1, v2, . . . , vn} n αivi = 0 i=1 α1 = α2 = . . . = αn = 0. E = {e1, e2, . . . , en} V v ∈ V B n v = αiei. i=1 V E = {e1, e2, . . . , en} F = { f1, f2, . . . , fm} V n = m B1 B2 B1 B2 n R n
xyz x y z u v w det (u; v; w) u v w i j k v = 〈v1, v2, v3〉 . i = 〈1, 0, 0〉 j = 〈0, 1, 0〉 k = 〈0, 0, 1〉 v = v1 i + v2 j + v3 k. 0 = 0i + 0j + 0 k = 〈0, 0, 0〉 . u = u1 i + u2 j + u3 k v = v1 i + v2 j + v3 k u + v = (u1 + v1)i + (u2 + v2)j + (u3 + v3) k. u = u1 ·i + u2 · j + u3 · k αu = (αu1)i + (αu2)j + (αu3) k.
- Page 1: u v w u + v = v + u,
- Page 5 and 6: u = √ 2 v = √ 5 w = √ 13 6
- Page 7 and 8: = R⊕ x = R⊕ cos φ cos λ y =
- Page 9 and 10: u · v = v · u, u · (αv + β w
- Page 11 and 12: u = cos(θ1)i + sen(θ1)j v = cos(
- Page 13 and 14: u×v 2 det (u; v; u × v)
- Page 15: P ρ φ z z ρ
0 0 <br />
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u − v = u + (−1) · v. <br />
(−1) · v −v <br />
v + (−v) = v + (−1)v = (1 − 1)v = 0v = 0. <br />
<br />
α · v αv <br />
{v1, v2, . . . , vn} <br />
{α1, α2, . . . , αn} αi = 0 <br />
n<br />
αivi = 0<br />
i=1<br />
{v1, v2, . . . , vn} <br />
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n<br />
αivi = 0<br />
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i=1<br />
α1 = α2 = . . . = αn = 0.<br />
E = {e1, e2, . . . , en} <br />
V v ∈ V B<br />
n<br />
v = αiei.<br />
i=1<br />
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V E = {e1, e2, . . . , en} F = { f1, f2, . . . , fm} <br />
V n = m <br />
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B1 B2 <br />
B1 B2 <br />
n R n
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