For any linear map f: EE, lez D). If f2 = id, then /1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 27E
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For any linear map f: EE, let U+ = Ker ((id - f)) and let
U¯ = Im(½ (id – ƒ)). If ƒ² = id, then
U+ = Ker
((id - )) = m((id + 1)).
and so, f(u) =
=u on U+ and f(u) =
=-u on U-.
Transcribed Image Text:For any linear map f: EE, let U+ = Ker ((id - f)) and let U¯ = Im(½ (id – ƒ)). If ƒ² = id, then U+ = Ker ((id - )) = m((id + 1)). and so, f(u) = =u on U+ and f(u) = =-u on U-.
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