Let U be a unitary matrix. Prove: (a) U is normal. (b) If is an eigenvalue

Question:

Let U be a unitary matrix. Prove:
(a) U is normal.
(b) If λ is an eigenvalue of U, then |λ| = 1.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 01:02 AM

See More Questions

(a) Show that U is a unitary matrix if and only if U-1 = U . (b) Show that the following matrices are unitary and compute their inverses: (i) 1 12 2 12 1 G22 132i 1-12i -4 -2i 52-4 2i
(a) According to Exercise 5.2.12, the Grarn-Schmidt process can also be applied to produce orthonormal bases of complex vector spaces. In the case of Cn, explain how this is equivalent to the...
Let c = (c0, c1,... , cn-1)T Cn be the vector of discrete Fourier coefficients corresponding to the sample vector f = (f0, f1,..., fn-1)T. (a) Explain why the sampled signal f = Fn c can be...
The English publisher of a book called Cambridge gave a New York publisher permission to sell that book any place in the world except in England. The New York publisher made several bulk sales of the...
Lowell Company purchased a machine that has a manufacturer's suggested life of 18 years. The company plans to use the machine on a special project that will last 12 years. At the completion of the...
A bottled water distributor wants to determine whether the mean amount of water contained in 1 gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know...
The force which causes an aircraft to turn is controlled by which primary control surface: elevator, aileron, or rudder?
The controller at FT Industries has asked you, her new assistant, to analyze the following data related to projected and actual overhead costs for October: For October, the number of good units...
Consider this expression: val opt1 Some (20) val opt2 = Some(5) val opt format Some("%d/%d = %d") val z for { x
Case 1. Presented below are the financial balances for the BonGiovi Company and the Terens Company as of December 31, 2017, immediately before BonGiovi acquired Terens. Also included are the fair...
Given find a matrix B such that BHB = A. 2 oi 1
Show that if a matrix U is both unitary and Hermitian then any eigenvalue of U must equal either 1 or -1.
Which of the following is a prime cost? A. Indirect materials B. Direct labor C. Administrative expenses D. Factory depreciation expenses
The graph represents a labor market. What is the equilibrium hourly wage? What is the equilibrium number of hours worked? per hour increase in labor demanded decrease in labor demanded increase in...
Two independent companies, Vaughn Co. and Cullumber Co., are in the home building business. Each owns a tract of land held for development, but each would prefer to build on the other's land. They...
Pharmacy Compounding: The Good, the Bad and the Ugly. Please provide a detailed Kindly answer the following in details - A.) What is pharmacy compounding ? B.) Analysis of pharmacy compounding, i.e....
Your company is planning to have the pest control activity on second weekend of July (July 9 & July 10). As an office assistant write a memo in a courteous way to all the office staff keep their...
A woman is wallpapering a laundry room 9 ft by 9 ft by 9 ft high. How many square feet of paper will she need if there are 76 ft of openings in the room? The woman will need ft of wallpaper.
Because of a very significant scope limitation, the auditors are uncertain about the propriety of the clients accounting for deferred income taxes. The possible amounts involved are so significant...
Use a calculator to evaluate the expression. Round your result to the nearest thousandth. V (32 + #)
Let u and v be solutions to the homogeneous linear system Ax - 0. (a) Show that u + v is a solution. (b) Show that u - v is a solution. (c) For any scalar r, show that ru is a solution. (d) For any...
Justify Remark 1 following Example 6 in Section 2.2.
Show that if A is singular and Ax = b, b 0, has one solution, then it has infinitely many.
Provide the codification references to support your answers Scope Questions 1. Which entities are subject to the Interim Reporting guidance within the Codification? 2. Does the Foreign Currency...
Why should a company establish an internal control structure? (2 marks) Evaluate the advantages and disadvantages of Perpetual Inventory System against Periodical Inventory System respectively. (2...
The Green Chef is an exclusive restaurant in your city. Reservations are difficult to secure and the menu is expensive. The owner, Chef Jorge, is rumored to be running an illegal gambling operation...

Let U be a unitary matrix. Prove: (a) U is normal. (b) If is an eigenvalue

Question:

Step by Step Answer:

a U H U I UU H b If x ...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions