collegeblondewith#s
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- Apr 1, 2006
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My task for college is to shorten and generalize the following list of axioms for a vector space from 10 to 4 using abstract algebra. Any help would be very much appreciated.
thanx a bunch
1. The sum of u and v , denoted by u + v, is in V.
2. u + v = v + u.
3. (u+v) + w = u + (v + w).
4. There is a zero vector 0 in V such that u + 0 = u.
5. For each u in V, there is a vector -u in V such that u + (-u) = 0.
6. The scalar multiple of u by c, denoted by cu, is in V.
7. c(u + v) = cu + cv.
8. (c + d)u = cu + du.
9. c(du) = (cd)u.
10. 1u = u.
thanx a bunch
1. The sum of u and v , denoted by u + v, is in V.
2. u + v = v + u.
3. (u+v) + w = u + (v + w).
4. There is a zero vector 0 in V such that u + 0 = u.
5. For each u in V, there is a vector -u in V such that u + (-u) = 0.
6. The scalar multiple of u by c, denoted by cu, is in V.
7. c(u + v) = cu + cv.
8. (c + d)u = cu + du.
9. c(du) = (cd)u.
10. 1u = u.
