Use Eq. (12) to prove the Cauchy-Schwarz inequality: Show that equality holds if and only if w

Question:

Use Eq. (12) to prove the Cauchy-Schwarz inequality:

z(MA) - z||M||||A|| = ||MX A||

Show that equality holds if and only if w is a multiple of v or at least one of v and w is zero.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 31, 2023 04:39 AM

See More Questions

Use the proof of Theorem 8.5 to show that equality in the Cauchy-Schwarz Inequality holds if and only if x = 0, y = 0, or x is parallel to y.
Which level of staff would be involved in evidenced-based practice investigation or research?
The Sarbanes-Oxley Act of 2002 changed the complexion of the auditing profession in many ways. Discuss the impact the Act had on auditors with respect to criminal liability in the audits of public...
You firm needs to pay its British supplier 1,000,000. If the exchange rate is $1.61/, how many dollars will you need to pay the British supplier? OA. $1,000,000 OB. $621,118 c. $1,610,000 D. $385,787
Suppose your company will receive $100 million at t = 4 but must make a $107 million payment at t = 5. Assume the spot and forward rates from question 5. Show how the company can lock in the interest...
Failsafe Textiles employs three highly skilled maintenance workers who are responsible for repairing the numerous industrial robots used in its manufacturing process. A worker can fix one robot every...
What are some of the legal ramifications?
Selected comparative financial statements of Sugo Company follow. Required 1. Compute trend percents for all components of both statements using 2006 as the base year. Analysis Component 2. Analyze...
Royal International Bank (RIB) charges an interest rate of 1.25% per month on loans to its customers. Like all lenders, RIB must report an annual percentage rate (APR) to customers. What should the...
Show that if u, v, and w are nonzero vectors and (u v) w = 0, then either (i) u and v are parallel, or (ii) w is orthogonal to u and v.
Show that if a, b are nonzero vectors such that a b, then there exists a vector X such that a X = b
What accounting treatments are appropriate for investments in equity securities without readily determinable fair values?
Prepare a balance sheet in excel using the information below. Note not all may be needed for the completion of a balance sheet. Cash and cash equivalents Patient Revenue Short term investments...
An urn has 15 balls in it, including 3 green balls, 5 yellow balls and 7 red balls. Your statistics professor gives you the opportunity to draw two balls in succession (without replacement) in the...
On October 1st 2010, a US pharmaceutical company exporting to the UK knows that has an account receivable of 500,000 due on Friday, March 19th 2011. The following data is available: Spot rate (US...
A development company owns 90 acres of land in Scarborough where it intends to construct three high rise office buildings, four garden office buildings, plus a 4.5 million square foot shopping...
For the circuit below, use the approximation for gain in the passband for your calculations. Assume the components have the following values: Vs = 8 Vpp, Cf = 4 nF, Rf = 500 02, R = 1000 2 and w=2000...
Bob Wright is a skilled machinist who has identified a need for specialized, custom-made containers that store and move biological materials. This market is particularly active in Bob's community...
Define deferred revenue. Why is it a liability?
Solve the triangle. a 40 45 4.
Solve the triangle. 85 a 3 50
Solve the triangle. 125 10 30
(a) Let F be any field. Prove that if a b = 0 for some a, b = F, then a = =0 or b = 0. (b) Let S = {ff: RR} be a set of all real-valued functions defined on R under the usual addition and...
How much 8 % saline solution should Kent mix with 7 0 cc of a 1 7 % saline solution to produce a 1 3 % saline solution
Consider the equation y=x^(2)+5x-6. Determine whether the function has a maximum or minimum value. State the maximum or minimum value. What are the domain and range of the function

Use Eq. (12) to prove the Cauchy-Schwarz inequality: Show that equality holds if and only if w

Question:

z(M·A) - z||M||₂||A|| = ₂||MX A||

Step by Step Answer:

Transferring sides in Eq 12 we get Since vxw2 0 we have v w vw v w Taking the square ...View the full answer

Calculus

Students also viewed these Mathematics questions