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

Question:

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

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 18, 2016 08:52 AM

See More Questions

(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) Use mathematical induction to prove that, for n ¥ 2, the companion matrix C(p) of p (x) = xn + an-1xn-1 + ··· + a1x + a0 has characteristic polynomial (-1) np (A). (b)...
Let A be an n ( n matrix. (a) Show that det(A) is the product of all the roots of the characteristic polynomial of A. (b) Show that A is singular if and only if 0 is an eigenvalue of A. (c) Also...
Name each of the following compounds using R,S and E,Z (Section 3.5) designations where necessary: a. b. c. d. e. f. g. h. CH2CH3 H- CH3 H2CH C-C C-C CI Br CH,CH CH-CH,CH,CH, - H3C CH2CH2l CH2CH...
The following independent events for New Age Theatre Ltd. during the year ended November 30, 2012, require a journal entry for the dates mentioned below or an adjusting journal entry, or both. The...
Oakridge Leasing Corporation signs an agreement on January 1, 2020, to lease equipment to LeBlanc Limited. Oakridge and LeBlanc follow ASPE. The following information relates to the agreement. 1. The...
Discuss the criminal trial process.
Business Week recently ran an article on companies debt policies, and the names Modigliani and Miller (MM) were mentioned several times as leading researchers on the theory of capital structure....
2. Find the worst-case time complexity of the OpenMystery algorithm below. Input: n: positive integer 1 Algorithm: OpenMystery 2 Let open be a Boolean array of size n 3 Initialize open to false 4...
Work out a short-term financing plan for Dynamic Mattress Company, assuming the limit on the line of credit is raised from $38 to $50 million. Otherwise keep to the assumptions used in developing...
Show that tr A = 0 if and only if det etA = I for all t.
Show that the origin is an asymptotically stable equilibrium solution to if and only if Au
You are in-house general counsel of Coulomb Co., a manufacturer of electrical equipment. In the ordinary course of business you are copied on emails regarding a purchase contract for several million...
Income Statement Sales $250,000 Costs $120,000 Other Expenses $20,000 Depreciation $15,000 EBIT $95,000 Interest $29,000 Taxable Income $66,000 Taxes $23,100 Net Income $42,900 Dividends $12,870...
Company PQR is considering issuing new equity at a cost of 12%. The company's investment bank charges a 5% underwriting fee on the gross proceeds. Calculate the flotation cost as a percentage of the...
Describe the key steps and considerations involved in the successful deployment of an enterprise-wide risk management framework and its supporting capabilities within a large organization. Highlight...
Why does an elevated urinary level of VMA (a metabolite of epinephrine and norepinephrine) suggest the presence of a pheochromocytoma? Why is it necessary to do a 24-hour measurement of VMA, rather...
If Mrs. Byrnes urinary Na+ excretion had been measured, would you expect it to be higher than, lower than, or the same as that of a healthy person? Why? How was the saline infusion expected to help...
a. A vacant lot acquired for $115,000 is sold for $298,000 in cash. What is the effect of the sale on the total amount of the sellers (1) Assets, (2) Liabilities, and (3) Stockholders equity? b....
we have to compute the letter grades for a course. The data is a collection of student records stored in a file. Each record consists of a name(up to 20 characters), ID (8 characters), the scores of...
(a) Estimate the value of the limitx0 (1 + x) 1/x to five decimal places. Does this number look familiar? (b) Illustrate part (a) by graphing the function y = (1 + x)1/x
The slope of the tangent line to the graph of the exponential function y = 2x at the point (0, 1) is limx0 (2x 1)/x. Estimate the slope to three decimal places.
(a) Evaluate the function f(x) = x2 (2x/1000) for x = 1, 0.8, 0.6, 0.4, 0.2, 0.1, and 0.05, and guess the value of (b) Evaluate f(x) for x = 0.04, 0.02, 0.01, 0.005, 0.003, and 0.001. Guess again. 2*...
Use Pohlig-Hellman algorithm to compute log2 (19) modulo 37. Compute xi's directly, by computing sufficiently many powers of gi.
A shoe seller sold shoes worth 1 6 0 TL on the first day, 1 9 2 TL on the second day and 1 4 4 TL on the third day at the some price . At was t how many shoes were sold by the seller in 3 days?
The Financial Services is one of the important industries when KPMG operates in. What's the market structure of the Financial Services?. In addition, what's the level of concentration and barriers to...

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

Question:

Step by Step Answer:

Let ut e t v where v is the corresponding eigenvecto...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions