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

2012년 7월 30일 (월) 10:47 판

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

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

@@ 25번째 줄: / 25번째 줄: @@
 <h5>tensor algebra</h5>
+* <math>T(V)</math>
@@ 34번째 줄: / 34번째 줄: @@
 * 정의 <math>\Lambda(V) := T(V)/I</math>
-* <math>\Lambda(V) = \Lambda^0(V)\oplus \Lambda^1(V) \oplus \Lambda^2(V) \oplus \cdots \oplus \Lambda^n(V)</math>
+* grading <math>\Lambda(V) = \Lambda^0(V)\oplus \Lambda^1(V) \oplus \Lambda^2(V) \oplus \cdots \oplus \Lambda^n(V)</math>
 * <math>\alpha\wedge\beta = (-1)^{kp}\beta\wedge\alpha</math>
@@ 68번째 줄: / 68번째 줄: @@
 * [http://www.auburn.edu/%7Etamtiny/math7970-11f.html http://www.auburn.edu/~tamtiny/math7970-11f.html]
+* http://math.stackexchange.com/questions/157528/wedgekv-cong-mathrmaltkv?rq=1
 * Math Overflow http://mathoverflow.net/search?q=