Page 824 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 824
form an orthonormal basis for . Use Theorem 6.3.1 to express as a linear combination of these
vectors.
Prove that if u and v are vectors in a complex inner product space, then
37.
Prove: If is an orthonormal basis for a complex inner product space V , and if u and w are any vectors in
38. V, then
Hint Use Theorem 6.3.1 to express u and w as linear combinations of the basis vectors.
39. (For Readers Who Have Studied Calculus) Prove that if and are vectors in
complex then the formula
defines a complex inner product on .
40. (For Readers Who Have Studied Calculus) Let and be vectors in complex and let this space
have the inner product defined in Exercise 39. Find
(a)
(b)
(c)
41. (For Readers Who Have Studied Calculus) Let and be vectors in complex
and let this space have the inner product defined in Exercise 39. Show that the vectors , where ,,
, …, form an orthonormal set.
Copyright © 2005 John Wiley & Sons, Inc. All rights reserved.
