Question: (a) Prove that if is an eigenvalue of A, then n is an eigenvalue of An. (b) State and prove a converse if A

(a) Prove that if λ is an eigenvalue of A, then λn is an eigenvalue of An.
(b) State and prove a converse if A is complete. (The completeness hypothesis is not essential, but this is harder, relying on the Jordan canonical form.)

Step by Step Solution

★★★★★

3.42 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a If Av v then by induction A n v n v and hence v is an eigenvector wit... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

952-M-L-A-E (2637).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Prove: If A is an eigenvalue of A, x is a corresponding eigenvector, and 5 is a scalar, then -s is an eigenvalue of A - sI, -and x is a corresponding eigenvector.

(a) Prove that if 0 is a nonzero eigenvalue of A, then 1 / is an eigenvalue of A-1. (b) What happens if A has 0 as an eigenvalue?

Prove that if is an eigenvalue of A, then et is an eigenvalue of etA. What is the eigenvector?

Proof Creator 1 Problems MAT246 LEC0101, Fall 2021 Assignment Information Writing Tips: See the handout posted on the course website. Also the additional writing supports (writing centres, ELL...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Consider the following definitions: Definition The set of linked lists of natural numbers L is defined by: Basis Step: EL Recursive Step: If I EL and n E N, then (n.) EL Definition The function...

1. A geologist believes that a new process will extract gold from rock more effectively than the process that was used previously. She takes two random samples of gold-bearing rocks and treats the...

Please answer questions labeled (3) and the bonus part at the bottom. Please verify answers to (1) and (2).. Provide clear steps for my understanding. Thanks! Bonus - Answers to verify...

2.1 Homework 1) Label each of the following as a statement or as \"not a statement.\" If you find a statement, give its truth value. a) Take the highway. b) What time is it? c) Winston Churchill was...

Discrete Math Fall 2017 Homework 7 Due: Friday, November 10, 2017 The below problems involve material from Chapter 5. You must type your solutions. Submit a single PDF file on eLC by 9PM on the given...

(a) B marks Scenario 1 First Choice Home Loans Ltd is an Australian company that provides mortgage loans which are loans that are typically secured by the property of the borrower. First Choice Home...

Binge drinking survey. One reason that Normal distributions are important is that they describe how the results of an opinion poll would vary if the poll were repeated many times. About 20% of...

Assume the demand curve for Pepsi passes through the following two points: PRICE PER BOTTLE OF PEPSI NUMBER OF BOTTLES OF PEPSI SOLD $2.50 100 000 1.25 200 000 a Draw a graph with a linear demand...

Reconsider the situation in Exercise 10-22, part (a). Construct a confidence interval estimate for the difference in mean impact strength, and explain how this interval could be used to answer the...

A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film, and believes that this can be achieved by reducing the...

The melting points of two alloys used in formulating solder were investigated by melting 21 samples of each material. The sample mean and standard deviation for alloy 1 was x1 = 420oF and s1 = 4oF,...

A change in expected inflation affects both the supply and demand for bonds. True/False A change in the interest rate does not shift the demand for bonds. True/False 3. An increase in the expected...

Ghost, Inc., has no debt outstanding and a total market value of $185,000. Earnings before interest and taxes, EBIT, are projected to be $29,000 if economic conditions are normal. If there is strong...

attach excel in the answer QM0.2 a) The following table shows bets for several companies. Calculate each stock's expected rate of return in CAPM. Assume the risk free rate of interestis 9 percent....