Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Example 10: Define T: R" → R", x = (X1, X2,...,xn) → (X2, X3,..., Xn, 0), with the Euclidean norm. Then for each 0 x € R" we have ||Tx||2||×|| -|x1|² ||x||² = ||x||²/2 and therefore, ||T|| ≤ 1. Since ||T(0, X2, X3,...,xn) ||2 || (0, X2, X3,...,xn) ||2 ≤ 1, i.e. ||Tx||2 ≤ ||x||2, we get ||T|| 1. Hence, we must have ||T|| = = 1. Unable to understand this example. Are then some pinting mistakes also?

Example 10: Define T: R" → R", x = (X1, X2,...,xn) → (X2, X3,..., Xn, 0), with the Euclidean norm. Then for each 0 x € R" we have ||Tx||2||×|| -|x1|² ||x||² = ||x||²/2 and therefore, ||T|| ≤ 1. Since ||T(0, X2, X3,...,xn) ||2 || (0, X2, X3,...,xn) ||2 ≤ 1, i.e. ||Tx||2 ≤ ||x||2, we get ||T|| 1. Hence, we must have ||T|| = = 1. Unable to understand this example. Are then some pinting mistakes also?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 6E: 6. In Example 3 of section 3.1, find elements and of such that but . From Example 3 of section 3.1:...
See similar textbooks
icon
Related questions
Question
100%
Example 10: Define T: R" → R¹, x = (x1, x2,...,xn) the Euclidean norm. Then for each 0 ‡ x € R¹ we have |||Tx||_ ||×|| - |×1|² ||x||²/ ||x||² and therefore, ||T|| ≤ 1. Since ||T(0, X2, X3,..., Xn)||2 || (0, X2, X3,...,xn) ||2 = ≤ 1, i.e. ||Tx||2 ≤ ||X||2, we get ||T|| 1. Hence, we must have ||T|| = 1. (X2, X3,..., Xn, 0), with Unable to understand this example. Are there some pinting mistakes also?
Transcribed Image Text:Example 10: Define T: R" → R¹, x = (x1, x2,...,xn) the Euclidean norm. Then for each 0 ‡ x € R¹ we have |||Tx||_ ||×|| - |×1|² ||x||²/ ||x||² and therefore, ||T|| ≤ 1. Since ||T(0, X2, X3,..., Xn)||2 || (0, X2, X3,...,xn) ||2 = ≤ 1, i.e. ||Tx||2 ≤ ||X||2, we get ||T|| 1. Hence, we must have ||T|| = 1. (X2, X3,..., Xn, 0), with Unable to understand this example. Are there some pinting mistakes also?
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS