Solution Found!

Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams
Change Question

What are the eigenvalues and eigenvectors of a projection a reflection

Chapter 6, Problem 4

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

What are the eigenvalues and eigenvectors of a projection? a reflection?

Questions & Answers

QUESTION:

What are the eigenvalues and eigenvectors of a projection? a reflection?

ANSWER:

Problem 4

What are the eigenvalues and eigenvectors of a projection? a reflection?

                                                        Step by Step Solution

Step 1 of 2

Let  be a projection matrix. Then, by definition,

                 (i)

Suppose,  is an eigenvalues of. Then,

               (ii)

Multiplying both sides of equation (ii) by  

 

So, two eigenvalues of  are 0 and 1.

The eigenvector of corresponding to the eigenvalues 0 is the solution of the equation 

The eigenvector of  corresponding to the eigenvalues 1 is the solution of the equation 

Add to cart

Study Tools You Might Need

Chapter: 4 Problem: 38P

Physics with MasteringPhysics 4
Problem 38P What is the highest tree the ball in the previous problem could clear on its way to the longest possible holc-in-one? Reference (previous) Problem: . A golfer gives a ball a maximum initial speed of 34.4 m/s. (a) What is the longest possible hole-in-one for this golfer? Neglec

Chapter: 8 Problem: 8.91

Organic Chemistry 2
The following sequence of reactions was performed during a synthesis of (+)-coronafacic acid, a key component in the plant toxin coronatine (J. Org. Chem. 2009, 74, 24332437). Predict the product of this reaction sequence and justify the regiochemical outcome of the second reaction. 1) TsCl, pyridine

Chapter: Problem: 2

Myers' Psychology for AP 2
Which of the following best represents crystallized intelligence? a. Jake can solve math word problems quickly. b. Grandpa Milt is good at crossword puzzles. c. Aliyah has a knack for training dogs. d. Anna writes creative computer programs. e. Heng bakes excellent chocolate chip cookies.

Chapter: 7 Problem: 55

The Practice of Statistics 5
Bottling cola A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean \(\mu=298\) ml and standard deviation \(\sigma=3\) ml. (a) What is the proba

Chapter: 3 Problem: 5

Essentials of Statistics for the Behavioral Sciences 10
Using the following informal histogram, what is the value of the mean? Explain your answer.

Chapter: 2 Problem: 18

Psychology 1
The ________ is controlled by the experimenter, while the ________ represents the information collected and statistically analyzed by the experimenter. a. dependent variable; independent variable b. independent variable; dependent variable c. placebo effect; experimenter bias d. experiment bias; plac

Chapter: 12 Problem: 34

Biochemistry 9
The fidelity of protein synthesis is assured twice during protein synthesis. How and when?

Chapter: 16 Problem: 16.102

Chemistry 13
A 2.0-L kettle contains 116 g of boiler scale \(\left(\mathrm{CaCO}_{3}\right)\). How many times would the kettle have to be completely filled with distilled water to remove all of the deposit?

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back