Question: Prove that ||w1 + wa+ ||w1-wa= 2||wi|+2||wall for any w and wa in an inner product space W.

Prove that ||w1 + wa+ ||w1-wa= 2||wi|+2||wall for any w and wa 

Prove that ||w1 + wa+ ||w1-wa= 2||wi|+2||wall for any w and wa in an inner product space W.

Step by Step Solution

★★★★★

3.40 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Proof Let W be an inner product space and let w 1 w 2 W HNT 1 HNT 2 II w ... 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

Document Format (2 attachments)

PDF file Icon

636214674d5bb_236441.pdf

180 KBs PDF File

Word file Icon

636214674d5bb_236441.docx

120 KBs Word File

Students Have Also Explored These Related Mathematics Questions!

Q:

Prove that the norm on an inner product space satisfies ||cv|| = |c| ||v|| for any scalar c and vector v.

Q:

In an inner product space ||x + y||2 + ||x - y||2 = 2 ||x||2 + 2||y||2

Q:

Prove that for any u and v in an inner product space V ||u||2 + ||u - v||2 = 2||u||2 + 2||v||2 Give a geometric interpretation of this result for the vector space R2

Q:

Prove that the second bilinearity formula (3.4) is a consequence of the first and the other two inner product axioms.

Q:

4. Prove Theorem 2. [Hint: For any real and (> 0) compute the PDF of (U(r) )/ and show that the standardized U(r), (U(r) )/, is asymptotically N(0,1) under the conditions of the theorem.]

Q:

Can you make questions from this notes following the instruction given below? You are to make your "OWN" Multiple Choice Questions (MCQs) for all Topics from Introduction of Law and Obligations First...

Q:

Pruddy Plaintiff, who while at the Cannes film festival fainted at the sight of the people on the beach sunning without "any" protection, sued the hotel. Pruddy suffered extensive injuries from the...

Q:

Chapter 6.1 Write on paper for upvote. questions: 23, 25, 37, 41 please 10. U = [_3 31. =18 8] 27. a. (2v - w, 3u + 2w) b. llu + vil In Exercises 11-12, find the standard inner product on P2 of the...

Q:

30. If A and B are any two vectors in V,, prove that (A - B) x (A + B) = 2(A X B). In Exercises 31 and 32, use the cross product to find an equation of the plane containing the given three points....

Q:

Can you make questions base on the given instructions below and base on the notes. You are to make your "OWN" Multiple Choice Questions (MCQs) for all Topics from Introduction of Law and Obligations...

Q:

1. Do you agree with Crimson's conclusion that the lease term for the cargo vessel is one year because the revenue contract is for one year

Q:

A 6 in. sch 40 pipeline carries a petroleum fraction (viscosity $15 \mathrm{cP}, \mathrm{SG} 0.85$ ) at a velocity of $7.5 \mathrm{ft} / \mathrm{s}$, from a storage tank at $1 \mathrm{~atm}$ pressure...

Q:

A 2 in. sch 40 pipe carries $\mathrm{SAE} 10$ lube oil at $100^{\circ} \mathrm{F}(\mathrm{SG}=0.928)$. The flow rate may be as high as $55 \mathrm{gpm}$, and you must select an orifice meter to...

Q:

Two items both have reorder points with service levels of 99%. One of the items is ordered 10 times a year, and the other item is ordered 20 times a year. Do these two items have the same overall...

Q:

(a) Find one more nonzero term for each of the solutions y 1 (x) and y 2 (x) in Example 8. (b) Find a series solution y(x) of the initial-value problem y'' + (cos x)y = 0, y(0) = 1, y'(0) = 1. (c)...

Q:

Draw a schematic diagram of I.C. engines and name the parts.

Q:

please post answers with workings Q2(5): Prepare the journal entries to account for the 'hedge item' and 'the hedging instrument' for the year ended 31 December 2021. (25 marks) ACC20013 Company...

Q:

You deposit $10,000 in a savings account that earns 7.5% simple interest per year. What is the minimum number of years you must wait to double your balance? Suppose instead that you deposit the...

Q:

Let [u1, u2] and [v1, v2] be ordered bases for R2. Where (a) Determine the transition matrix corresponding to change of basis from the standard basis [e1,e2] to the ordered basis [111,112]. Use this...

Q:

Let Estimate the largest eigenvalue of A and a corresponding eigenvector by doing five iterations of the power method. You may start with any nonzero vector x0. 3 4

Q:

If a, b, and c are floating - point numbers, then fl(fl(a + b) + c) = fl(a + fl(b + c)) In the case of a true statement, explain or prove your answer. In the case of a false statement, give an...

Q:

The Baton Rouge Company compiled the following information for the current year related to its defined benefit pension plan: Present value of defined benefit obligation, beginning of year .....

Q:

On January 1, Year 1, the Hoverman Corporation made amendments to its defined benefit pension plan, resulting in $150,000 of past service costs. The plan has 100 active employees with an average...

Q:

On January 2, Year 1, Argy Company's board of directors granted 12,000 stock options to a select group of senior employees. The requisite service period is three years, with one-third of the options...