linear algebra proof thanks Let V be an inner product space. Suppose that TE L(V). For u, v € Vdefine (u, v)T by(u, v)T = (Tu, v).Prove that (,) defines an inner product on V if and only if T is an invertible positiveoperator.

Introduction: An invertible positive operator is a linear operator on a vector space that is both…

Answered: Let V be an 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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linear algebra proof

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Let V be an inner product space. Suppose that TE L(V). For u, v € V
define (u, v)T by
(u, v)T = (Tu, v).
Prove that (,) defines an inner product on V if and only if T is an invertible positive
operator.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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