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?

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
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
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS