If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q

Question:

If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also orthogonal.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-0538735452

3rd edition

Authors: David Poole

See More Books

Question Posted: Nov 13, 2018 12:11 PM

See More Questions

Let Q be an orthogonal matrix. (a) Prove that if is an eigenvalue, then so is 1/. (b) Prove that all its eigenvalues are complex numbers of modulus || = 1. In particular, the only possible real...
Prove that the transpose of an orthogonal matrix is an orthogonal matrix.
If is an orthogonal matrix, find all possible values of a, b, and c. [1/2
March is a month of variable weather in the Northeast. The chart below records the actual high and low temperatures for a selection of days in March from the weather report for Pittsburgh,...
The market demand for cigarettes are given in the following table. Price ($ per pack) ......................... 6.506.005.505.004.504.003.50 Quantity (packs per day) .......................... 40 50...
For the network of Fig. 7.92, determine: a. IDQ and VGSQ. b. VDS and VS. 16 V 2.2 k 1a DSs6 mA DS 2.2 k 6-4 V
The following table gives the vapor pressure of water for various temperatures a. Plot a scatter diagram. Does it seem likely that a straight-line model will be adequate? b. Fit the straight-line...
Kara owns 35% of the KLM Partnership and 45% of the KTV Partnership. Lynn owns 20% of KLM and 3% of KTV. Maura, Karas daughter, owns 15% of KTV. No other partners own an interest in both partnerships...
Suppose, you want to start a small business. prepare at least 5 slides on what is your small business and outline some of the requirements to create and maintain it. What are few strategies to become...
A major pharmaceutical wholesaler buys brand drugs from a manufacturer at wholesale prices and sells them to pharmacies at retail prices. It estimates that the wholesale (W) price, the retail (R)...
Consider the following genetically controlled bio synthetic pathway for pigments in the flowers of a hypothetical plant: Assume that gene A controls the conversion of a white pigment, P 0 , into...
(a) Prove that an orthogonal 2 Ã 2 matrix must have the form where is a unit vector. (b) Using part (a), show that every orthogonal 2 Ã 2 matrix is of the form where 0 ¤ u...
Computer algebra systems sometimes need a helping hand from human beings. Ask your CAS to evaluate 2x 4x 1dx. If it doesnt return an answer, ask it to try 2x 22x 1dx instead. Why do you think it...
What is this savings bank's total required level of legal reserves? How much must the bank hold on a daily average basis with the Federal Reserve bank in its district? 12. R, W, & B Savings Bank...
2. Ahmed has OMR 5,000 to invest for three years period, He has five investment alternatives. What will be the amount after three years from the flowing alternatives? i. Bank deposit at 5% ii. Bond...
2. Draw the demand curve for an environmental service, for example carbon sequestration (process of capture and long-term storage of atmospheric carbon-dioxide) from tree planting and discuss what...
Questions are regarding Inter Parfums Corporate. 1. Business and Strategy (briefly describe Inter Parfums Corporate and Business Strategy; research their website, annual reports and investors...
4. If fixed costs are $100 and variable costs are $200 at an output level of 30 units, what are the average fixed costs, average variable costs, and average total costs? *Please show all work this...
Refer to all of the facts in Problem 12-3. Required 1. Prepare a statement of cash flows for 2014 using the indirect method in the Operating Activities section. 2. On the basis of your statement in...
Discuss the concept of the looking-glass self. how do you think others perceive you? do you think most people perceive you correctly?
Suppose we want to use the procedure in Problem 8.49 using a one-sided test in which the alternative hypothesis is that men have higher cholesterol levels than women. State the hypotheses being...
Perform the test in Problem 8.66 for the medical therapy group, and report a p-value? Cardiology A clinical trial compared percutaneous transluminal coronary angioplasty (PTCA) with medical therapy...
What test can be performed to compare the mean change in duration of exercise between the two treatment groups? Cardiology A clinical trial compared percutaneous transluminal coronary angioplasty...
In the Queries section of the Navigation Pane, right-click Stone Mountain Patients to select it and display the shortcut menu. 3. Click Copy on the shortcut menu. 4. Right-click the empty area near...
What is 'audit risk', and discuss/analyze the components of audit risk. b. List the four (4) things involved in the initial audit planning and which should be done early in the audit.
K Internal control is a plan of organization and a system of procedures, implemented by company. A. external auditors; management B. external auditors; board of directors OC. internal auditors;...

If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q

Question:

Step by Step Answer:

Let Q PQ be obtained by rearranging the rows of ...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Mathematics questions