1. Suppose that TEL(V) satisfies T2 = T. Show that T is an orthogonal projection iff T is self-adjoint.
1. Suppose that TEL(V) satisfies T2 = T. Show that T is an orthogonal projection iff T is self-adjoint.
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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![1. Suppose that T = L(V) satisfies T2 = T. Show that T is an orthogonal
projection iff T is self-adjoint.
2. Find g € R[r]<2 so that f f(x)g(x) dx = f f(x) cos(x)dx for all ƒ €
R[x] <2.
3. Suppose that T = L(V) is self adjoint. Let v € V, A € F and > 0 be
so that ||v|| = 1 and ||Tv - Av|| < E. Show that there is an eigenvalue X' with
|X-X'| <E.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff04438c7-4e55-45d6-9636-5c6e57ab97dc%2F4df0aaa2-3ba0-4ed4-923b-c3965bee6772%2Fueinzb_processed.png&w=3840&q=75)
Transcribed Image Text:1. Suppose that T = L(V) satisfies T2 = T. Show that T is an orthogonal
projection iff T is self-adjoint.
2. Find g € R[r]<2 so that f f(x)g(x) dx = f f(x) cos(x)dx for all ƒ €
R[x] <2.
3. Suppose that T = L(V) is self adjoint. Let v € V, A € F and > 0 be
so that ||v|| = 1 and ||Tv - Av|| < E. Show that there is an eigenvalue X' with
|X-X'| <E.
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