Question: Let A be a real square matrix and eA its exponential. Under what conditions does the linear system have an asymptotically stable equilibrium solution?

Let A be a real square matrix and eA its exponential. Under what conditions does the linear system have an asymptotically stable equilibrium solution?

Step by Step Solution

★★★★★

3.52 Rating (176 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

According to Exercise 9421 the eigenvalues of e ... 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 (2808).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let A be a real 2 ( 2 matrix with complex eigenvalues = a ( bi such that b 0 and ( ( = 1. Prove that every trajectory of the dynamical system xk+1 = Axk lies on an ellipse. [Hint: Theorem 4.43...

Let A be a real 2 Ã 2 matrix with the property that a21a12 > 0, and let Compute B = SAS-1. What can you conclude about the eigenvalues and eigenvectors of B? What can you conclude about the...

Let A be a real 3 x 3 matrix, and assume that the linear system has a periodic solution of period P. Prove that every periodic solution of the system has period P. What other types of solutions can...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

For monotone functions f, f0: P Q between posets (P, vP ) and (Q, vQ), let f v f(i) Prove that the binary relation v is a partial order. [3 marks] (ii) For monotone functions between posets p : P 0...

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

2.7. Explicit Solutions to Dierential Equations 109 power (kw) 20 15 10 5 0 08:00 10:00 12:00 14:00 16:00 time 18:00 2.7 Explicit Solutions to Dierential Equations In the very rare case in which an...

ESE 500: Homework 3 Due on October 16 (Monday) Part A: Matrix Exponential Problem 1. Without using Matlab, compute eAt , using two of your favourite methods, for: \u0014 \u0015 0 2 A= 1 2 It is...

Least Squares Approximation Hector D. Ceniceros 1 Least Squares Approximation Let f be a continuous function on [a, b]. We would like to find the best approximation to f by a polynomial of degree at...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Presented below are selected data from the financial statements of Debonair Corp. for 2009 and 2008. Required: Calculate the dividend payout ratio for2009. 2009 2008 $123,000 Net income Cash...

Using the information in E20-13 about Linda Berstler Companys defined benefit pension plan, prepare a 2010 pension worksheet with supplementary schedules of computations. Prepare the journal entries...

Most managers adopt particular styles to simplify their decision making This helps them make sense of information Why do you think these styles are unreliable explain about this topic with web link

Writing in the New York Times, Simon Johnson, an economist at MIT, makes the argument that people outside the United States may at some point decide to save less (in which case they may hold onto...

Use a graph to estimate the equations of all the vertical asymptotes of the curve y = tan (2sin x)

(a) Use numerical and graphical evidence to guess the value of the limit (b) How close to 1 does have to be to ensure that the function in part (a) is within a distance 0.5 of its limit? x'- 1 lim .3

Given that lim x→ a f(x) = 3 lim x→ a g(x) = 0 lim x→ a h(x) = 8 Find the limits that exist, if the limit does not exist, explain why. (a) lim [f(x) + h(x)] (b) lim [f(x)]? (c) lim...

HELPPLZ each year for 10 years. How much money should you plan to deposit in your retirement each year? Instead of using Solver, use PV and PMT to solve for annual deposit:...

A B D E F E17-2 (LO 1, 2, 4) Weighted Average Number of Shares Gogeon Inc. is publicly traded and uses a calendar year for financial reporting. The company is authorized to issue 50 million common...

2. Asuma que las transacciones del mes de noviembre, para KAT. Co., son las siguientes \begin{tabular}{|l|l|l|} \hline & a. & Recibi efectivo por $60,000 de los inversionistas a cambio de acciones...