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Example 2.8.3 Let G = SO(2), the group of all 2 x 2 real matrices which are orthogonal, that is, they satisfy the relation AA' = I, and which have determinant 1. The set G is in one-to-one correspondence with the unit circle in R2 by the map %3D (x1, 22) - -x2

Example 2.8.3 Let G = SO(2), the group of all 2 x 2 real matrices which are orthogonal, that is, they satisfy the relation AA' = I, and which have determinant 1. The set G is in one-to-one correspondence with the unit circle in R2 by the map %3D (x1, 22) - -x2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Example 2.8.3 Let G = are orthogonal, that is, they satisfy the relation AA' = I, and which have determinant 1. The set G is in one-to-one correspondence with the unit circle in R? by the map S(2), the group of all 2 x 2 real matrices which x2 (#1, #2) → (. -x2
Transcribed Image Text:Example 2.8.3 Let G = are orthogonal, that is, they satisfy the relation AA' = I, and which have determinant 1. The set G is in one-to-one correspondence with the unit circle in R? by the map S(2), the group of all 2 x 2 real matrices which x2 (#1, #2) → (. -x2
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