MAT 150A Study Guide - Final Guide: Bijection, Identity Function, Permutation Matrix

• School: UC-Davis
• Department: Mathematics
• Course: MAT 150A
• Professor: José Simental Rodríguez

Document Summary

Announcements: oh next week only, oct 1-5, mwf 4-5. Recall: elements of sn are bijective functions p = {1, , n} {1, , n, product in sn corresponds to composition of functions. Example (12) s3 = p(1) = 2. = p(3) = 3 say (12) s4, is (12)(3)(4) (12)(34) ? (12)(13)3, (12) = p, (13) = q p(q(1)) = p(3) = 3. 1 3 2 1 p(q(3)) = p(1) = 2 (12)(13) = (132) (13)(12) = (123) thus,(13)(12) Example (1598)(43)(279)(421) s9 p1 = (1598), p2 = (43), p3 = (279), p4 = (421) p1(p2(p3(p4(1)))) = p1(p2(p3(4))) = p1(p2(4)) = p1(3) = 3 p1(p2(p3(p4(3)))) = p1(4) = 4. Do you want me to do more example? (no) [pause] let me do one more example. The identity element e sn is the identity function: e(1) = 1, e(n) = n, e(2) = 2, (12)(12) = e is that ne with you? if that is not ne with you then, oh well.