Let (, ) be an inner product in the vector space V. Given an isomorphismT : U H V, Put [u, v] = (Tu, Tv), for any U, V E U. Check thatl Jis an in-house product. Note: From the internal product (:) define a new "internal product (with the mentioned conditions) the inner product axioms must be verified in this new function (u, v] = (Tu, Tv)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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linear algebra 

Let (:) be an inner product in the vector space V. Given an isomorphismT : U - V. Put
[u, v] = (Tu, Tv), for any u, V E U. Check thatl:lis an in-house product.
Note:
From the internal product (:) define a new "internal product (with the mentioned conditions)
the inner product axioms must be verified in this new function (u, v] = (Tu, Tv)
i [uiv]=[viu]
i [uru,w] = [uw] +[viw]
ii. Cauiu] =x [uiv]
N. [uiu] 7O
Yu
[uiu] =0 u=0
Transcribed Image Text:Let (:) be an inner product in the vector space V. Given an isomorphismT : U - V. Put [u, v] = (Tu, Tv), for any u, V E U. Check thatl:lis an in-house product. Note: From the internal product (:) define a new "internal product (with the mentioned conditions) the inner product axioms must be verified in this new function (u, v] = (Tu, Tv) i [uiv]=[viu] i [uru,w] = [uw] +[viw] ii. Cauiu] =x [uiv] N. [uiu] 7O Yu [uiu] =0 u=0
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