Suppose v1, , vn forms an eigenvector basis for the complete matrix A, with 1, , n the corresponding eigenvalues Prove that every eigenvalue of A is one of the 1, , n ...

Suppose v1, ..., vn forms an eigenvector basis for the complete matrix A, with 1, ..., n

Question:

Suppose v1, ..., vn forms an eigenvector basis for the complete matrix A, with λ1, ..., λn the corresponding eigenvalues. Prove that every eigenvalue of A is one of the λ1, ..., λn.

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 17, 2016 09:07 AM

See More Questions

Let u1,...,un be an orthonormal basis of Rn. Prove that it forms an eigenvector basis for some symmetric n n matrix A. Can you characterize all such matrices?
Find the eigenvalues and an orthonormal eigenvector basis for the following symmetric matrices: (a) (b) (c) (d) (e) 7 2 3 3 (3 3) 2 -1 -1 5 431 013 104 461
Define the shift map S: Cn Cn by S(v1, v2, ..., vn-1, vn)T = (v2, v3, ..., vn, v1)T. (a) Prove that S is a linear map, and write down its matrix representation A. (b) Prove that A is an orthogonal...
Required A. Calculate Mr. Worthy's minimum employment income for the current year. B. Assume Mr. Worthy had only $4,000 in commission income in addition to his $65,000 salary. Calculate Mr. Worthy's...
What are the elements of a cause of action in strict product liability?
Singh, a qualified appraiser of fine art and other collectibles, was advising Colleen when she was determining the amount of the charitable contribution deduction for a gift of a sculpture to a...
Identify the mode for each of the following sets of data: a. 7, 3, 7, 1, 7 b. 3, 1, 1, 2, 3, 3 c. 8, 22, 8, 10, 9, 8, 12, 7, 8 d. 5, 3, 6, 4, 5, 3, 1, 5, 2, 5, 6, 5 e. 11, 9, 13, 6, 14, 12, 7, 12,...
The following are selected transactions of Lindblom Company. Lindblom prepares financial statements quarterly. Jan. 2 Purchased merchandise on account from Evers Company, $20,000, terms 2/10, n/30....
At December 3 1 , 2 0 2 2 , Samson Company reported Accounts Receivable of $ 1 0 5 , 0 0 0 and Allowance for Doubtful Accounts of $ 7 , 5 0 0 . On January 7 , 2 0 2 3 , Delilah, Inc. declares...
Troys Tires sells a certain brand tire which has a daily demand that is normally distributed, with a mean of 15 tires and a standard deviation of 4 tires. (In your model use integers for all...
(a) Prove that if A is complete, so is A2. (b) Give an example of an incomplete matrix A such that A2 is complete.
Let L = L*: Rn Rn be a self-adjoint linear transformation with respect to the inner product (.). Prove that all its eigenvalues are real and the eigenvectors are orthogonal.
What is a government company?
How much more deposits can the bank attract without breaking the minimum capital requirement and lend out to mortgage borrowers at the similar risk level?
The legacy of war identifies that all of the following cities except what is the one were spared from any major damage?
What does John Hale's testimony tell you about the social environment insalem?
when problem solving, your suppliers sort activities by answering three questions. They include what was different this time; why here and not there? What is another question that a supplier might...
When one of Allison's fellow employees explains that they will be missing work for a few weeks because their mother is terminally ill, what is the primary type of listening that Allison is using?
According to a survey in December 2018 of Women on Boards, women hold 21.7% of director seats on U.S. corporate boards. This study also reports that 39.2% of U.S. companies have three or more female...
A seasonal index may be less than one, equal to one, or greater than one. Explain what each of these values would mean.
Consider Supplemental Exercise 10-85. Suppose that the true difference in mean fill volume is as much as 2 fluid ounces; did the sample sizes of 10 from each vineyard provide good detection...
A Rockwell hardness-testing machine presses a tip into a test coupon and uses the depth of the resulting depression to indicate hardness. Two different tips are being compared to determine whether...
Two different gauges can be used to measure the depth of bath material in a Hall cell used in smelting aluminum. Each gauge is used once in 15 cells by the same operator. (a) State any assumptions...
Assignment 1 1. Write a program to implement the following formula for a -10 and b = 4; result = (a + 2b - 4ab)^4 // ^4 means to the power of 4 (1 mark) 2. Write a program to implement result = sin...
I have most of it done, I just need help fixing some things. import java.util.Scanner; public class Main { private String[] database; private Scanner input; public Main() { database = new...
Part 2 - WeatherMonitor Suppose you observe daily temperatures and want to know how hot each day is compared to recent days. That is, you want to: keep track of daily temperature values and know for...

Suppose v1, ..., vn forms an eigenvector basis for the complete matrix A, with 1, ..., n

Question:

Step by Step Answer:

Suppose Av v Write The...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions