MAT 150A Study Guide - Final Guide: Linear Map, Surjective Function, Unit Circle

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Enumerating the vertuces if a regular n-gon gives a homomorphism. 6 )) = (123456) hexagon on unit circle enumerated ccw starting with 1 at (1,0) 1 3 5, 2 4 6 is (rot( 4 re (0) = (26)(35) re ( . 6 ) = (12)(36)(45) another hex (similar layout) enumerated by the 3 diagonals. X y = (a x ) (a y ) A x = x1ae1 + + xnaen since linear operators. X xiyi(aei aej) = x xiyi i,j=1 (cid:4) If x , y rn, d( x , y ) = || x y || = p( x y ) ( x y ) Let a on, then x , y rn, d( x , y ) = d(a x , a y ) A function f : rn rn is called an isometry if x , y rn, d( x , y ) = d(f ( x ), f ( y ))

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