If A has a dominant eigenvalue 1, prove that the eigenspaces E1 is one-dimensional.

Question:

If A has a dominant eigenvalue λ1, prove that the eigenspaces Eλ1 is one-dimensional.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

See More Books

Question Posted: Apr 15, 2016 06:16 AM

See More Questions

A common misconception is that if A has a strictly dominant eigenvalue, then, for any sufficiently large value of k, the vector Akx is approximately equal to an eigenvector of A. For the three...
A matrix A is given along with an iterate x 5 , produced as in Example 4.30. (a) Use these data to approximate a dominant eigenvector whose first component is 1 and a corresponding dominant...
If G = (V, E) is an undirected graph with |V|-n and |E| = k, the following matrices are used to represent G. Let V = {v1, v2, . . . , Define the adjacency matrix A = (aI j)nÃn where aIJ = 1 if...
State DMV records indicate that of all vehicles undergoing emissions testing during the previous year, 70% passed on the first try. A random sample of 200 cars tested in a particular county during...
Dipoto Companys balance sheet shows Inventory $162,800. What additional disclosures should be made?
The interface 2x + y = 8 between two media carries no current. If medium 1 (2x + y > 8) is nonmagnetic with H1 = 4ax + 3ay az A/m. Find: (a) The magnetic energy density in medium 1, (b) M2 and B2...
Describe surrogacy and the legal and ethical issues that can arise.
Presented here are liability items for O'Brian Inc. at December 31, 2017. Prepare the liabilities section of O'Brians balance sheet. Accounts payable Notes payable $157000 FICA taxes payable 7,800...
21. DOES THE U.S DOLLAR INDEX WEAKEN IF THE US GROWTH ACCELERATES ? 22. THE U.S DOLLAR INDEX WEAKEN IF THE INTEREST RATE DIFFERENTIALS NARROW BETWEEN THOSE NATIONS ?
Suppose that in a production of spark plugs the fraction of defective plugs has been constant at over a long time and that this process is controlled every half hour by drawing and inspecting two...
Let be an eigenvalue of A with corresponding eigenvector x. If a and is not an eigenvalue of A, show that 1 / ( - ) is an eigenvalue of (A - al)-1 with corresponding eigenvector x. (Why must A =...
In Exercises 47-50, draw the Gerschgorin disks for the given matrix. 1. 2. 3. 4. 012 5 140 0.1 2 210 2 0 1-5i 2i i1+0 -2i 5 i 0 0 16 8 014 618 12 416 0 2-4 0 0
The primary purpose of managerial accounting is to provide information useful for management decisions. Many of the managerial accounting techniques that you learn in this course will be useful for...
List at least five reasons explaining the popularity of workplace teams.
Tired of long, boring meetings, some companies have embraced five-minute huddles or desk drive-bys for minor decision making. The CEO of a New York digital agency likes to cut people short when they...
Put yourself in the shoes of an employment recruiter. Youre impressed by a job candidates rsum and references. During her interview, she responded well and asked insightful questions about the...
Etiquette expert Jacqueline Whitmore offers this advice to aspiring speakers: A long, dry presentation of facts is sure to be a yawn-inducer, so consider your presentation as a conversation with your...
You recently complained to your boss that you were unhappy with a piece of equipment you use (printer, computer, copier, scanner, or the like). After some thought, the boss decided that your...
Do investors always invest money in companies to make a profit?
What is your assessment of the negotiations process, given what you have studied? What are your recommendations for Mr. Reed? You must justify your conclusions
Determine which equations are linear equations in the variables x, y, and z. If any equation is not linear, explain why not. 2x - xy - 5z = 0
Determine which equations are linear equations in the variables x, y, and z. If any equation is not linear, explain why not. 3 cos x - 4y + z = 3
Determine which equations are linear equations in the variables x, y, and z. If any equation is not linear, explain why not. (cos 3) x - 4y + z = 3
How do change interventions leverage advanced methodologies such as appreciative inquiry, design thinking, and complexity science to foster a holistic understanding of change dynamics, unlock latent...
what extent do change interventions leverage digital technologies, data analytics, and artificial intelligence to enhance change effectiveness, monitor change progress, and facilitate real-time...
Consider a project that requires spending of $15,000 immediately and generates $6,000 per year for the next 4 years (assume each $6,000 comes at the end of each year).What is the NPV of this project?...

If A has a dominant eigenvalue 1, prove that the eigenspaces E1 is one-dimensional.

Question:

Step by Step Answer:

If 21 is dominant then for all other eigenvalues But ...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Linear Algebra questions