13) Let V be a complex vector space. Suppose that T is a self-adjoint operator on a inner-product space V such that there exists v E V with ||v|| = 1 such that (T(v), v) > 1. Prove that there exists an eigenvalue of T which is larger than 1.
13) Let V be a complex vector space. Suppose that T is a self-adjoint operator on a inner-product space V such that there exists v E V with ||v|| = 1 such that (T(v), v) > 1. Prove that there exists an eigenvalue of T which is larger than 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![13) Let V be a complex vector space. Suppose that T is a self-adjoint operator on a inner-product space
V such that there exists v E V with ||v|| = 1 such that (T(v), v) > 1. Prove that there exists an
eigenvalue of T which is larger than 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0548f28d-2867-4ce8-91e2-809a65372be3%2Fdf0649b3-1e30-492d-b08d-f423ffb13a34%2Ficxj5a_processed.png&w=3840&q=75)
Transcribed Image Text:13) Let V be a complex vector space. Suppose that T is a self-adjoint operator on a inner-product space
V such that there exists v E V with ||v|| = 1 such that (T(v), v) > 1. Prove that there exists an
eigenvalue of T which is larger than 1.
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