Question: Let x, y R n . Under which condition on R n does the function define an inner product on R n

Let x, y ∈ Rn. Under which condition on ∝ ∈ Rn does the function 

P f(x,y) = axxxyk k=1

define an inner product on Rn?

P f(x,y) = axxxyk k=1

Step by Step Solution

★★★★★

3.37 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

The axioms of 22 are all satisfied for any R n except the conditions These p... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Optimization Models Questions!

Q:

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

Q:

Assigment-2 1. Let U = (, , 4) and 1 = (1, 1, 13). Show that the expression does not define an inner product on R, and list all inner product ariom that fail to hold @

Q:

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...

Q:

1 1. (6+4+4+6) Let P3 denote the vector space of all third degree or less polynomials. (a) Find two linearly independent vectors in P3 that interpolate the data points (1, 2), (2, 1) and (3, 2). (b)...

Q:

,, kindly solve Consider the Linear Regression Model 1. For any X = x, let Y = x8 + U, where B E R*. 2. X is exogenous. 3. The probability model is { f (u; ) is a distribution on R : E, [U] = 0, Var,...

Q:

Set #22 MATH 110 : 2015-16 Due: Friday, 18 March 2016 1. The population of Canada, as determined by the Canadian census, was as follows: year 1991 1996 2001 2006 2011 population (in millions) 27.3...

Q:

NAME______________ Preactice Exam for MATH 3210 Directions: A main focus of this course is that each person develop the logical processes necessary to explain/prove their results in a clear, precise...

Q:

4 ECE 5759 Problem 1. Due: October 25 Closed Convex set in the space of Matrices (10 marks) nn A matrix A R is called a positive semidefinite matrix if xT Ax 0 for every x Rn . Prove that the set of...

Q:

Provide solutions to the following attachments. Question 1 There are 10,000 identical individuals in the market for commodity X, each with a demand function given by Qodx = 12 - 2Px, and 1000...

Q:

Kindly give only correct answers showing your steps 1. (a) Use the Intermediate Value Theorem to show that the equation - sin (x) + sin(x) =-1 has at least two distinct real solutions on (0, ce)....

Q:

A foreigner manufacturing company is considering to open a plant in Turkey. This company has estimated 5-year net present value for each city under three different future economic/political climate...

Q:

Consider the following facts: Water freezes spontaneously at 25C and 1 atm, and ice has a more ordered structure than liquid water. Explain how a spontaneous process can lead to a decrease in entropy.

Q:

If beta is 0.9, sigma_m [standard deviation of the market] is 0.2, and sigma[e_a], which is the standard deviation of the idiosyncratic risk is 0.3, What is the total risk sigma_A If beta is 0.9,...

Q:

7.3 Explain the roles of self-disclosure and emotional expression in maintaining face-to-face and online relationships

Q:

Based on the box plot, does the arithmetic mean or the geometric mean provide a more appropriate measure of location for this type of data?

Q:

What does A 1 A 2 mean? Consider a family with a mother, father, and two children. Let A 1 = {mother has influenza}, A 2 = {father has influenza}, A 3 = {first child has influenza}, A 4 = {second...

Q:

What does A 1 A 2 mean? Consider a family with a mother, father, and two children. Let A 1 = {mother has influenza}, A 2 = {father has influenza}, A 3 = {first child has influenza}, A 4 = {second...

Q:

Atlantis Fisheries issues zero coupon bonds on the market at a price of $ 5 3 7 per bond. Each bond has a face value of $ 1 , 0 0 0 payable at maturity in 1 7 years. What is the yield to maturity for...

Q:

Homework: Ass... Question 11, P8-4 (simil... HW Score: 45.51%, 6.37 of 14 points Part 1 of 5 Save Points: 0 of 1 Hyperion Inc., currently sells its latest high-speed color printer, the Hyper 500, for...

Q:

3. Freeman buys a stock for $30 and at the same time a 3-month at-the-money put option for $2.15. The riskfree rate is 6% convertible semiannually. Calculate the spot price at expiration for which...