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theorem 1.31 The set of all rotations about the origin and reflections in lines through the origin is a group called orthogonal group and is denoted by O(2). SO(2) is a subgroup of index 2 in O(2). Det'n: Let P be any point in E². The set P of all lines that passes through P is called pencil of lines through P. We denote REF(P) : REF(P) the smallest group of isometries containing all , wherele P. We denote ROT(P) the set of all rotations about P.

theorem 1.31 The set of all rotations about the origin and reflections in lines through the origin is a group called orthogonal group and is denoted by O(2). SO(2) is a subgroup of index 2 in O(2). Det'n: Let P be any point in E². The set P of all lines that passes through P is called pencil of lines through P. We denote REF(P) : REF(P) the smallest group of isometries containing all , wherele P. We denote ROT(P) the set of all rotations about P.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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theorem 1.31 The set of all rotations about the origin and reflections in lines through the origin is a group called orthogonal group and is denoted by 0(2). SO(2) is a subgroup of index 2 in O(2). Det'n: Let P be any point in E². The set P of all lines that passes through P is called pencil of lines through P. We denote REF(P) : REF(P) the smallest group of isometries containing all 24, where l e P. We denote ROT(P) the set of all rotations about P.
Transcribed Image Text:theorem 1.31 The set of all rotations about the origin and reflections in lines through the origin is a group called orthogonal group and is denoted by 0(2). SO(2) is a subgroup of index 2 in O(2). Det'n: Let P be any point in E². The set P of all lines that passes through P is called pencil of lines through P. We denote REF(P) : REF(P) the smallest group of isometries containing all 24, where l e P. We denote ROT(P) the set of all rotations about P.
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