Question: Prove that does not define an inner product on the vector space C°[ - 1, 1]. Explain why this does not contradict the fact that

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 it define an inner product on the subspace P(n)

f&)f(x)g(x) dx

Step by Step Solution

★★★★★

3.39 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If fx is any nonzero function that satisfies fx 0 for all 0 x 1 then f f 0 An example is the funct... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

952-M-L-A-E (1935).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

(a) Prove that the space R consisting of all infinite sequences x = (x1,x2,x3,...) of real numbers Xi R forms a vector space. (b) Prove that the set of all sequences x such that Form a subspace....

(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)

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

Suppose (v ,w) defines an inner product on a vector space V. Explain why it also defines an inner product on every subspace W V.

Rombes Physics 1B: PSet 2 PROBLEM I Problem 1 Orthogonal Functions 8: Fourier Decomposition In lecture, we mentioned that sinusoidal travelling waves provide \"building blocks\" out of which all...

Question 5. Does the formula |x]] := x define a norm on RR? Question 6. Show that the following formula defines an inner product on the vector space of all man matrices. (A, B) := trace (A B)....

Please help me with these 2 problems, thank you!!! Question 8. Show that the following formula defines an inner product on the vector space of all mxn matrices. (A, B) := trace(AT B). Question 9. Is...

Exercise 20. We define an inner product on a complex vector space V as a function that associates a complex number u,v to each pair of vectors u,v in V, such that the folowing axioms hold for all...

9, DUE Friday, March 24th, 2017 Hand in Part A and Part B as two separate assignments. Include the following information in the top left corner of every assignment: your full name, instructor's last...

Let V denote the vector space C [-1, l] of continuous real-valued functions on the closed interval [- 1, 1]. So, for example, the functions ET and cos(z) :r:2 belong to this vector space (where both...

For an expansion into new markets, NewTech Building Ltd plans to raise $66 million to finance this expansion. The company will issue new shares of equity through a general cash offering to raise the...

Calculate the probability that no triple among n random 32-bit integers sums to 0, and give an approximate estimate for n equal to 1000, 2000, and 4000. Give an approximate formula for the expected...

Pharcah Corporation purchased for $ 2 0 0 , 0 0 0 a 2 5 % intesst in Murghy. Inc. This investment enabies Pharowh to fourt significant infuence over Murphy. During the yeac, Mughy earned net income...

Describe Johnson Controls evolving policy on lead exposure.

Consider the vector space Rn with inner product (x. y) = xTy. For any n n matrix A, show that (a) (Ax, y) = (x, ATy) (b) (ATAx, x) = ||Ax||2

Show that equation (2) defines an inner product on Rmn.

Show that the inner product defined by equation (3) satisfies the last two conditions of the definition of an inner product.

true or false Moral relativists believe that their values are best, and so , insist on others acting in accordance with those values without compromise in every situation.

Assume that the corporate tax rate is 34% and the personal tax rate is 30%. The founders of a newly formed business are debating between setting up the firm as a partnership versus a corporation. The...

Consider the following information for Evenflow Power Co., Debt: 3,500 5.5 percent coupon bonds outstanding, $1,000 par value, 22 years to maturity, selling for 102 percent of par; the bonds make...