Question: Show that the identity u, v =1/4 || u + v || 2 1/4 || u v || 2 holds for vectors in

Show that the identity ⟨u, v⟩ =1/4 || u + v || 2 – 1/4 || u – v || 2 holds for vectors in any inner product space.

Step by Step Solution

★★★★★

3.46 Rating (149 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To show that the identity langle u v angle frac14 left u v ight2 frac14 left u v ight2 holds for vec... 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 Mathematics Questions!

Q:

1. (10 Points.) Calculate the line integral F.T ds. where F = (.+ 2y + x) and C is the curve comprised of line segments that go from (1, 3) to (17,51) to (41, 12) to (14,76) to (7,11). 2. (10...

Q:

Show that the identity function IX (example 2.5) is strictly increasing.

Q:

In this exercise, we show that any inner product (, ) on Rn can be reduced to the dot product when expressed in a suitably adapted basis. (a) Specifically, prove that there exists a basis v1,..., v"...

Q:

What will the following code segment print out? string[] words = {"One", "Two", "Three"); ArrayList wordList = new ArrayList (); wordList.addAll (Arrays.asList (words)); wordList.add("Four");...

Q:

2. Let there be the set V which is defined to be V = y ( t ) | d - y (t ) + y(t) = 0, t E [0, 27], y(0) = yo, = yo where yo, yo ER dy(t) (a) Recall the vector space (C' [0, 27], R) from homework 2:...

Q:

Solve all 5 problems on paper. Show all work I) show that the following functions define an inner product ou IR, where U = ( x , , y , ) and V = ( x 2, yz ) a ) = 3 x , x 2 + y , 4 2 b) = XIXz + 4,...

Q:

Can you please help me with number 31. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.7 Matrix Exponentials and Linear...

Q:

(a) Find the transition matrix S from B' to B. (b) Use the matrices S and A to find [v], and [T(v)], where [V]B/ = (-1,4) T. (c) Find S" and A' (the matrix for T relative to B' ). (d) Find [T(v)]B,...

Q:

6 Chapter 6. Intentional Torts and Business Torts (15 points) Directions: 1. 2. Read the attached ad: ! Publication of an ad parody, which appeared in a 1983 issue of Hustler Magazine. Jerry Falwell...

Q:

Question 3 Let W be a subspace of R3 spanned by the two vectors 4 3 u: 3 ,v= 3 2 5 The following two questions are related to the subspace W. Question 3.1 Find a basis for the orthogonal complement...

Q:

During April, the first production department of a process manufacturing system completed its work on 300,000 units of a product and transferred them to the next department of these transferred...

Q:

Brookingdale Insurance Company has expressed interest in being represented by Roger's insurance agency. For each of the following items of information about Brookingdale, describe the sources of...

Q:

How might the current economic situation with the job market, wage rate, or other economic factor impact your organization in a positive or negative sense?

Q:

2. Not all is lost with Tesla's production issues. Tesla has left a door (and a few windows) open for competitors to take part of the market. Which manufacturers stand to gain the most? Why?

Q:

Determine a mainline airline's fare structure. Discussion can include mock data on the fare structure that you outline for business vs pleasure travel, passenger demand patterns, Seasonal operations,...

Q:

Since the 2016 presidential election, there have been multiple changes to the Patient Protection and Affordable Care Act (ACA). What are they and how have they impacted healthcare access, cost, and...

Q:

Timothy, as an option trader, is constantly looking for opportunities to make an arbitrage transaction. Assume Timothy observed the following prices for options on CMC stock: $4.15 for a call with an...

Q:

Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin. Passes through (2, 2) and (1, 4)

Q:

Redo Exercise 4.3.1 using (a) the weighted inner product (v, w) = 2v1w1) + 4v2w2 + 3v3w3, (b) the inner product (v, w) = vTC w based on the positive definite matrix 9 121 210

Q:

For each of the following augmented matrices write out the corresponding linear system of equations. Solve the system by applying Gaussian Elimination to the augmented matrix. (a) (b) (c) (d) 2 31 3...

Q:

Let R2 be a bounded domain. Let C() denote the vector space consisting of all continuous, bounded real-valued functions f(x, y) defined for (x, y) 2.

Q:

A random sample of size 20 yields = 3.13 and s2 = 1.45. Calculate a confidence interval for the population mean whose confidence level is as follows: a. 0.99 b. 0.98 c. 0.95 d. 0.90 e. 0.80 f. What...

Q:

Required Tasks: 1. Prepare a descriptive analysis of the data using charts, graphs, and numerical measures. 2. Construct and interpret a 95% confidence interval estimate for the mean weight for male...

Q:

Paper-R-Us is a national distributor of printer and copier paper for commercial use. The data file called Sales contains the annual, year-to-date sales values for each of the companys customers....