"외대수(exterior algebra)와 다중선형대수(multilinear algebra)"의 두 판 사이의 차이

2012년 7월 30일 (월) 09:25 판

정의 \(\Lambda(V) := T(V)/I\)
\(\Lambda(V) = \Lambda^0(V)\oplus \Lambda^1(V) \oplus \Lambda^2(V) \oplus \cdots \oplus \Lambda^n(V)\)
\(\alpha\wedge\beta = (-1)^{kp}\beta\wedge\alpha\)

\(A_k(V)\) : the set of k-alternating forms on V
\(f:V^k\to{\mathbb R},\qquad f(v_{\sigma(1),\cdots,v_{\sigma(k)}})=(\text{sgn}\sigma)f(v_1,\cdots,v_k) \quad\text{for all} \quad\sigma\in S_k.\)
\(\Lambda^k(V^{*})\simeq\Lambda^k(V)^{*}\)
\(A_k(V)\simeq\Lambda^k(V)^{*}\)

(Λ^kV)^∗

Λ^k(V^∗)

@@ 39번째 줄: / 39번째 줄: @@
+* <math>A_k(V)</math> : the set of k-alternating forms on V
+* <math>f:V^k\to{\mathbb R},\qquad f(v_{\sigma(1),\cdots,v_{\sigma(k)}})=(\text{sgn}\sigma)f(v_1,\cdots,v_k) \quad\text{for all} \quad\sigma\in S_k.</math>
 * <math>\Lambda^k(V^{*})\simeq\Lambda^k(V)^{*}</math>
 * <math>A_k(V)\simeq\Lambda^k(V)^{*}</math>