Answered: 3. Let V be a complex inner product…

3. Let V be a complex inner product space and T: V→ V a linear transformation. Suppose that T satisfies the following property Vu € V, (T(u), u) = 0 Show that T = 0.

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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Question

3. Let V be a complex inner product space and T: V → V a linear transformation. Suppose that T satisfies
the following property
(T(u), u) = 0
Show that T = 0.
Vu € V₂

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