Does either of the following define an inner product on C[0, 1 ]? (a) = f(0)g(0) +

Question:

Does either of the following define an inner product on C°[0, 1 ]?
(a) = f(0)g(0) + f(l)g(l)
(b) (f.g) = f(0)g(0) + f(l)g(l)
+ f-10 f(x)g(x)dx

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 08:36 AM

See More Questions

Prove that does not define an inner product on the vector space C°[ - 1, 1]. Explain why this does not contradict the fact that it defines an inner product on the vector space C°[0, 1 ]. Does...
The cross product of two vectors in R2 is defined as the scalar V x w = v1w2 - v2w1 (3.22) for v = (v1, v2)T, w = (w1, w2)T. (a) Does the cross product define an inner product on R2? Carefully...
(a) Prove the inner product axioms for the weighted inner product (3.15), assuming w(x) 0 for all a x b. (b) Explain why it does not define an inner product if w is continuous and w(xo) < 0 for...
Here are the supply and demand equations for throstles, where p is the price in dollars: D (p) = 40 p S (p) = 10+p. On the axes below, draw the demand and supply curves for throstles, using blue...
Comment briefly on the main functions of management?
()ki (ompany pays $204,000 lor e(|uipmenl expected lo Iasi lour years and have a $20,000 salvage value. Prepare journiil enirics lo record Ibe rollowing costs relaled lo (be e(|uipnienl. 1. I fill...
91.17
The Vaughan audit team completed its audit field work on February 15, 2010. A conference was held on that date involving members of the audit firm and Bronys Bikes management. Participants in the...
Budget Preparation Collins Company is preparing its master budget for April. Use the given estimates to determine the amounts necessary for each of the following requirements. (Estimates may be...
A 450-mm-long AISI 1020 steel rod is subjected to a tensile load of 55 kN. The allowable tensile stress is 140 MPa and the allowable total elongation is not to exceed 0.2 mm. Calculate the required...
Which of the following formulas for (f, g) define inner products on the space C°[ - 1, 1 ]? a. b. c. d. Fee f(x)g(x)e dx f(x) g(x)x dx f (x)g(x) (x + 2) dx f(x)g(x)x2 dx
Let f(x) be a function, and ||f|| its L2 norm on [a,b]. Is ||f2|| = ||f||2? If yes, prove the statement. If no, give a counterexample.
Very few negotiable instruments are ever securitized. a. True b. False
What Is Chemical Energy? Definition and Examples
The fundamental concern of computer science is determining what can and cannot be automated. The earliest foundations of what would become computer science predate the invention of the modern digital...
History of the United States
United States History Pearl Harbor attack
List all the different formulas for an octahedral complex made from a metal (M) and three different ligands (A, B, and C). Describe any isomers for each complex.
Express these numbers in standard notation. a. 2.87 10-8 b. 1.78 1011 c. 1.381 10-23
In C[0, 1], with inner product defined by (3), consider the vectors 1 and x. Compute ||1 - p||, ||p||, ||1|| and verify that the Pythagorean Law holds.
In C[-, ], with inner product defined by (6), show that cos mx and sin nx are orthogonal and that both are unit vectors. Determine the distance between the two vectors.
Write out the Fourier matrix F8. Show that F8P8 can be partitioned zinto block form: F4 DAFA F4 -D,F
Questien It Calraluta bae neark yoe cen atforal to berren
In calculating the net present value of a proposed project, the cash flows of the project should include a.) amortization of goodwill b.) interest expenses paid to bondholders c.) extra working...
If Yolanda's insurance company cancels her fire insurance policy after 204 days, how much of the $682.00 annual premium will she receive as a refund (in $)? (Round you answer to the nearest cent.) $

Does either of the following define an inner product on C[0, 1 ]? (a) = f(0)g(0) +

Question:

Step by Step Answer:

a No positivity doesnt hold since if f0 f1 0 then f f 0 even if fx 0 for ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions