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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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