Let u = (u1, u2, u3)T R3 be a unit vector. Show that Qn = 2uuT

Question:

Let u = (u1, u2, u3)T ∈ R3 be a unit vector. Show that Qn = 2uuT - I represents rotation around the axis u through an angle π.

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

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 09:00 AM

See More Questions

Let u R3 be a unit vector. (a) Explain why the elementary reflection matrix R = I - 2uuT represents a reflection through the plane orthogonal to u. (b) Prove that R is an orthogonal matrix. Is it...
Use the Runge-Kutta method for systems to approximate the solutions of the following systems of first-order differential equations, and compare the results to the actual solutions. a. u'1 = 3u1 + 2u2...
Let B = {u1, u2, u3} be a basis for a vector space V, and let T: V V be a linear operator such that Find [T]B², where B² = {v1, v2, v3}, is the basis for V defined by v1 = u1, v2 = u1 + u2,...
A rectangular pontoon 10m long 7m broad & 2.5m deep weights 686.7KN. It carries on its upper deck an empty boiler of 5m diameter weighing 588.6 KN. The centre of gravity of the boiler and pontoon are...
What elements are necessary for an effective offer? What are some examples of non offers?
Refer to the original data in the preceding exercise. Poolsides management estimates that the number Preparation of Budgeted of subscribers in September should fall 10 percent below August levels,...
Much less clear are the processes by which the link is made, for example how, why and in what context? Commitment, motivation and job satisfaction are currently seen to have a key role. lo1
Consider the data in the Excel file Nuclear Power. Use simple linear regression to forecast the data. What would be the forecasts for the next 3 years?
Which of the following combinations of changes would result in the current ratio increasing by approximately 19%? A.) Current assets +8%; Current liabilities -5% B.) Current assets -8%; Current...
Distinguish between compatible and mapped addresses and explain their applications.
Draw the parallelogram spanned by the vectors Then draw its image under the linear transformations defined by the following matrices: 2 2and3 1.2 12 0 0')) 12 24
Let a R3 be a fixed vector and let Q be any 3 3 rotation matrix such that Qa = e3. (a) Show that, using the notation of (7.23), R = QT Z Q represents rotation around a by angle . (b) Verify this...
Find dy/dx by implicit differentiation. x sin y + y sin x = 1
Verify the results of Eq. (14.48) for the properties of the chiral projection operators. Data from Eq. 14.48 P = P+ P+ + P = 1 P_P+ P+P = 0 Py" = y P
Prove that the estimating equations in (11.13) are unbiased under MCAR, but are generally biased without the stringent MCAR assumption. (x) [y - f (xt;)] = 0, i=1 (11.13)
Refer to Figure 11.5: Which is the most expensive subcontract for this project? How much were the costs for the general contractor's crews for item 4? Figure 11.5 Division 1 2 3 4 5 6 7 Work Gen'l...
a. Using observations on the change in consumption $D C_{t}=C_{t}-C_{t-1}$ and the change in income $D Y_{t}=$ $Y_{t}-Y_{t-1}$ from 1959Q3 to 2015Q4, obtained from the data file cons_inc,...
Water at $20^{\circ} \mathrm{C}$ flows by gravity from a large reservoir at a high elevation to a smaller one through a 35-m-long, 5-cm-diameter cast iron piping system that includes four standard...
Some countries, such as Costa Rica, have no army. On the Internet, find the list of countries that have no standing army. Using that information, identify the factors that allow these countries to...
Research an article from an online source, such as The Economist, Wall Street Journal, Journal of Economic Perspectives, American Journal of Agricultural Economics, or another academic journal. The...
A confidence interval estimate is desired for the gain in a circuit on a semiconductor device. Assume that gain is normally distributed with standard deviation = 20. (a) Find a 95% CI for when n = 10...
Consider the gain estimation problem in Exercise 8-4. How large must n be if the length of the 95% CI is to be 40?
Following are two confidence interval estimates of the mean of the cycles to failure of an automotive door latch mechanism (the test was conducted at an elevated stress level to accelerate the...
The company sold merchandise to a customer on March 31, 2020, for $100,000. The customer paid with a promissory note that has a term of 18 months and an annual interest rate of 9%. The companys...
imer 2 0 2 4 Question 8 , PF 8 - 3 5 A ( similar to ) HW Score: 0 % , 0 of 1 0 0 points lework CH 8 Part 1 of 6 Points: 0 of 1 5 Save The comparative financial statements of Highland Cosmetic Supply...
An investor wants to purchase a zero coupon bond from Timberlake Industries today. The bond will mature in exactly 5.00 years with a redemption value of $1,000. The investor wants a 12.00% annual...

Let u = (u1, u2, u3)T R3 be a unit vector. Show that Qn = 2uuT

Question:

Step by Step Answer:

If v is orthogonal to u then u T v 0 and so Q v v ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions