Define the shift map S: Cn Cn by S(v1, v2, ..., vn-1, vn)T = (v2, v3,
Question:
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 matrix.
(c) Prove that the sampled exponential vectors ω0, ...., ωn-1 in (5.90) form an eigenvector basis of A. What are the eigenvalues?
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (8 reviews)
a b A T A I by direct computation or equivalently the columns o...View the full answer
Answered By
Mustafa olang
Please accept my enthusiastic application to solutionInn. I would love the opportunity to be a hardworking, passionate member of your tutoring program. As soon as I read the description of the program, I knew I was a well-qualified candidate for the position.
I have extensive tutoring experience in a variety of fields. I have tutored in English as well as Calculus. I have helped students learn to analyze literature, write essays, understand historical events, and graph parabolas. Your program requires that tutors be able to assist students in multiple subjects, and my experience would allow me to do just that.
You also state in your job posting that you require tutors that can work with students of all ages. As a summer camp counselor, I have experience working with preschool and kindergarten-age students. I have also tutored middle school students in reading, as well as college and high school students. Through these tutoring and counseling positions, I have learned how to best teach each age group. For example, I created songs to teach my three-year-old campers the camp rules, but I gave my college student daily quizzes to help her prepare for exams.
I am passionate about helping students improve in all academic subjects. I still remember my excitement when my calculus student received her first “A” on a quiz! I am confident that my passion and experience are the qualities you are looking for at solutionInn. Thank you so much for your time and consideration.
4.80+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
The difference map : Cn Cn is defined as = S - I, where S is the shift map of Exercise 8.2.13. (a) Write down the matrix corresponding to A. (b) Prove that the sampled exponential vectors w0,...
-
Define the sequence (cn) and (sn) inductively by c1(x) := 1, s1(x):= x, and for all n N, x R. Reason as in the proof of Theorem 8.4.1 to conclude that there exist functions c : R R and s : R R such...
-
Suppose V1, V2, . . . , Vn are independent noncentral 2 random variables having r1, r2, . . . , rn degrees of freedom, respectively, and with noncentrality parameters 1,2, . . . , n. Find the...
-
The AND function can be realized by using only n number of NOR gates. The value of nequal to
-
What is a security interest? What is the most common method of perfecting a security interest under Article 9?
-
When we said that your SO 3 reaction was stuck, we meant that it had stopped. Did it really stop, and how does your answer help explain why we can also describe the reaction as being in a state of...
-
La Bartolomeo Systems currently has an allcash credit policy. It is considering making a change in the credit policy by going to terms of net 30 days. Based on the following information, what do you...
-
Financial information for Gallup Inc. is presented below. Instructions Prepare a schedule showing a horizontal analysis for 2014 using 2013 as the baseyear. Current assets Plant assets (net) Current...
-
Identify situations that do not involve material right. 1. Tiffany provides a customer with 25% discount coupon during the period when it offers 10% discount to all other customers. 2. Homey Inc....
-
To clarify the results of the preceding problem, we look at a simpler example. a. Compute the arithmetic mean value for each system using X as the reference machine and then using Y as the reference...
-
Let be a real eigenvalue of the real n n matrix A, and v1, ..., vk a basis for the associated eigenspace V Suppose w Cn is a complex eigenvector, so Aw = w. Prove that w = c1 v1 + ... + ckvk is a...
-
(a) Compute the eigenvalues and corresponding eigenvectors of (b) Compute the trace of A and check that it equals the sum of the eigenvalues. (c) Find the determinant of A and check that it is equal...
-
For f(x) = ab x , is f(1), f(2), f(3) an arithmetic sequence or a geometric sequence? What is the common difference (or common ratio)?
-
How do a time draft and a sight draft differ?
-
Fill in the Blank. The transfer function is the _________ of the generalized impedance.
-
What are the different types of letters of credit?
-
Discuss the techniques available to reduce transaction exposure.
-
Why do firms use countertrade? What problems do they face when they do?
-
Less than 1.96 In assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a...
-
1. Below is depicted a graph G constructed by joining two opposite vertices of C12. Some authors call this a "theta graph" because it resembles the Greek letter 0. a. What is the total degree of this...
-
We can use the gambling interpretation given in Exercise 28 to find the expected number of tosses required to reach pattern B when we start with pattern A. To be a meaningful problem, we assume that...
-
In Example 11.11, define f(i) to be the proportion of G genes in state i. Show that f is a harmonic function (see Exercise 27). Why does this show that the probability of being absorbed in state...
-
It is raining in the Land of Oz. Determine a tree and a tree measure for the next three days weather. Find w(1),w(2), and w(3) and compare with the results obtained from P, P2, and P3.
-
Responsibilities of Management for the Financial Statements Management is responsible for the preparation and fair presentation of the financial statements in accordance with accounting principles...
-
Ryan incurred the following expenses this year: Criminal Restitution (fine paid) for DUI $27,000 arrest Bribe paid for dock permit to the County Inspector $1,000 Kickback paid to obtain University of...
-
Alexander Corporation sells its only product for $30 per unit. Its variable costs per unit are 40% of its selling price. Its total fixed costs for the year are $450,000. The company has an average...
Study smarter with the SolutionInn App