(1) (a) Suppose V is a real inner product space and u, v e V. Prove that if ||u + o||2 = ||u||? + ||v|2, then u and v are orthogonal. (b) Show by an example that (a) need not be true if V is a complex inner product space.
(1) (a) Suppose V is a real inner product space and u, v e V. Prove that if ||u + o||2 = ||u||? + ||v|2, then u and v are orthogonal. (b) Show by an example that (a) need not be true if V is a complex inner product space.
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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