MAT 150A Study Guide - Final Guide: Unit Circle, Dihedral Group

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

Document Summary

Let m matn n(r) then m on i it"s columns form an orthonormal collection. {ai} form an orthonormal collection of vectors in rn today studying o2 and so2 (cid:4) On = {m mat(n n)|m 1 = m t} A = (cid:20)a11 a12 a21 a22(cid:21) o2 = (cid:20)a11 a21(cid:21) and (cid:20)a12 a22(cid:21) choose an arbitrary point on the unit circle degrees from the right a21(cid:21) = (cid:20)cos (cid:20)a11 sin (cid:21) cos (cid:21) A = (cid:20)cos sin sin det(a) = 1 a so2. Refers to the rotation for initial point to 90 degrees counterclockwise. Cos (cid:21) (cid:20) sin the point 90 degrees clockwise. A = (cid:20)cos sin cos (cid:21) sin . Refers to rotation 90 degrees clockwise det(a) = 1 a 6 so2. A is a rotation by radians counterclockwise cos (cid:21) A = (cid:20)cos sin sin cos (cid:21) Re (cid:18) sin sin cos (cid:21) sin sin cos (cid:21) O2 = {rot( )| [0, 2 )} {re ( )| [0, )}