Question: Prove that if is an eigenvalue of A with multiplicity k, then etA is an eigenvalue of etA with the same multiplicity. Combine the

Prove that if λ is an eigenvalue of A with multiplicity k, then etA is an eigenvalue of etA with the same multiplicity. Combine the Jordan canonical form (8.51) with Exercises 9.4.17. 28.

Step by Step Solution

★★★★★

3.40 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If J is a Jordan matrix then by the arguments in Exercise 9428 e tJ is upper triangular 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 (2814).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

(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?

(a) Show that if is an eigenvalue of A then k is an eigenvalue of Ak. (b) What is wrong with this proof generalizing that? "If is an eigenvalue of A and is an eigenvalue for B, then is an...

(a) Prove that if is an eigenvalue of A, then n 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...

\fsh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Math 280 Strategies of Proof Fall 2007 Class Notes 3.6 Proving Conditional Statements II: Indirect Proofs In Section 3.4, we studied...

in here P(A) is power set of(A) 1.Prove that A B iff P (A) P (B). 2. Prove that for any set A, A = P (A). 3. Suppose {Ai | i I} and {Bi | i I} are indexed families of sets. (a) Prove that iI (Ai...

1) Deline symmetric Eroup and prove that every sex can be expressed uniquely as a product of cycles 2) Show that the group of symmetries of an equilateral triangle has order and find its centre a)...

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Help! Data Structure problem List.java import java.util.Random; import java.util.function.BiFunction; import java.util.function.Function; class EmptyListE extends Exception {} abstract class List {...

The last three picture Consider a two-person household. These two people have very similar preferences (that's why they enjoy living together), which are described by the following utility...

Last Updated: July 18, 2016 American Mock Trial Association MIDLANDS RULES OF EVIDENCE Article I. Rule 101. Scope; Definitions (a) Scope. These rules apply to proceedings in the courts of the State...

You have been hired as a forensic accountant to investigate a case of embezzlement. You have obtained the following information: The company had $500,000 in cash at the beginning of the year. The...

Why should you always carry out a residual analysis as part of a regression model? Discuss.

Alternative procedures that would provide evidence of the existence of receivables would include which of the following? a . Analysis of the aged trial balance. b . Physical observation of customer...

Let F(x) = x2 1 / |x 1| (a) Find (i) limx1+ F(x) (i) limx1 F(x) (b) Does limx1 F(x) exit? (c) Sketch the graph of F.

Let (a) Evaluate each of the following limits, if it exists. (i) limx→1+ h(x) (ii) limx→0 h(x) (iii) limx→1 h(x) (iv) limx→2- h(x) (v) limx→2+ h(x) (vi) limx→2 h(x) (b)...

(a) If the symbol [ ] denotes the greatest integer function defined in Example 10, evaluate (i) lim x2+ [x] (ii) lim x2 [x] (iii) lim x2.4 [x] (b) If n is an integer, evaluate (i) lim x n [x] (ii)...

An insurance company must make payments to a customer of $ 1 2 million in one year and $ 6 million in three years. The yield curve is flat at 8 % . a . If it wants to fully fund and immunize its...

What is the difference between American and European Options? American options are trading on American exchanges, while European options are trading on European exchanges exclusively. American...

Problem 9 - 1 7 Comparing Investment Criteria ( LO 1 , 2 , 3 , 5 , 7 ) Consider the following two mutually exclusive projects:Year 0 1 2 3 4 Cash Flow ( A ) - 5 3 5 0 , 0 0 0 4 5 , 0 0 0 6 5 , 0 0 0...