Answered: Let V be a finite dimensional, complex…

Let V be a finite dimensional, complex inner product space and let U be a subspace of V. Suppose v e V satisfies, (v, u) + (u, v) < (u, u) for all u E U. Prove that v E U-,

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Note: U- denotes the orthogonal complement of U, defined as,
U- = {v € V : (v, u) = 0 Vu E U}
%3D
%3D

Let V be a finite dimensional, complex inner product space and let U be a subspace of V.
Suppose v e V satisfies,
(v, u) + (u, v) < (u, u)
for all u E U. Prove that v E U-,

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