Prove that if A is a diagonalizable matrix such that every eigenvalue of A is either 0

Question:

Prove that if A is a diagonalizable matrix such that every eigenvalue of A is either 0 or 1, then A idempotent (that is, A2 = A).

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 06:15 AM

See More Questions

Prove that if A is a diagonalizable matrix with only one eigenvalue , then a is of the form A = l. (Such a matrix is called a scalar matrix).
(a) Show that if D is a diagonal matrix with nonnegative entries on the main diagonal, then there is a matrix S such that S2 = D. (b) Show that if A is a diagonalizable matrix with nonnegative...
If A is a diagonalizable matrix and all of its eigenvalues satisfy || < 1, prove that A'' approaches the zero matrix as n gets large.
Calculate the managerial remuneration from the following particulars of Zen Ltd. the company has only one Managing Director. Net Profit Net Profit is calculated after considering the following:...
Kevin Farley, an auditor with Koews CPAs, is performing a review of Knight Companys Inventory account. Knight did not have a good year, and top management is under pressure to boost reported income....
Consider the conducting plates shown in figure. If V(z = 0) = 0 and V(z = 2 mm) = 50 V, determine V, E, and D in the dielectric region (?r = 1.5) between the plates and ?s on the plates. A = (p =...
Discuss why a patients responsibilities are as important as his or her rights.
Russell Retail Group begins the year with inventory of $ 55,000 and ends the year with inventory of $ 45,000. During the year, the company has four purchases for the following amounts. Purchase on...
Estimate the 5 - day 9 9 % VaR for the portfolio assuming that its annual volatility calculated on the basis of weekly returns from the most recent 1 - year time window is 3 1 . 7 5 % .
Globalization and technology developments have led to some significant changes in the global economy. Discuss the importance of such changes to the United States. What is the impact upon supply...
Let A and B be similar matrices. Prove that the geometric multiplicities of the eigenvalues of A and B are the same.
In Exercises 5-7, a diagonalization of the matrix A is given in the form P-1 AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. 1. 2. 3. - 2 21 2 3101 0 0 1 1 -11 1012 0-1...
Lipitor is a drug designed to lower cholesterol levels. With current sales of Lipitor exceeding $13 billion each year, it has become the best selling drug ever. One dosage level of Lipitor is...
While interviewing applicants, questions are often asked by recruiters about qualifications. Your Task. Revise the above sentence to avoid dangling and misplaced modifiers.
How long should paragraphs be?
Tracking devices are being installed by many companies to gather real-time information on how employees interact. Your Task. Business writing is more forceful when it uses active-voice verbs. Revise...
When is the indirect strategy appropriate, and what are the benefits of using it?
Valuable insider information about a companys culture, interview procedures, and day-to-day activities is available for those who take the time to search. Enterprising job seekers check YouTube...
Marvin Company is a subsidiary of Hughes Corp. The controller believes that the yearly allowance for doubtful accounts for Marvin should be 2% of net credit sales. Given the recession and the high...
Citing a scientific article, explain in your own words, how DNA fingerprinting has been used in forensic science to solve crimes and why it may not always be accurate or effective.
Perform the indicated calculations. [2, 1, 2] + [2, 0, 1] in Z 3 3
Perform the indicated calculations. [2, 1, 2] [2, 2, 1] in Z 3 3
Perform the indicated calculations. [2, 0, 3, 2] ([3, 1, 1, 2] + [3, 3, 2, 1]) in Z 4 4 and in Z 4 5
Milligan's Backyard Storage Kits, a mail order company, sells a variety of backyard storage unit kits and landscaping decorations to its customers. Although the company makes a profit, David...
1. If you think about then Guest Services Essentials class, what do you believe to be the biggest change in your customer service practice? 2. Name and describe two customer service techniques to...
Packaging Waste & Recycling UK, 2013('000 tonnes) 2,260 Total Packaging Waste Total Recycled 4,000 3,868 3,459 3,000 2,339 2,000 1,639 1,029 1,000 806 714 462 436 23 0 0 Metal Glass Wood Paper...

Prove that if A is a diagonalizable matrix such that every eigenvalue of A is either 0

Question:

Step by Step Answer:

If D P 1 AP and D is diagonal then every entry of D is eith...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Linear Algebra questions