Let U be a unitary matrix. Prove: (a) U is normal. (b) If is an eigenvalue
Question:
(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:
Answer rating: 71% (14 reviews)
a U H U I UU H b If x ...View the full answer
Answered By
Susan Juma
I'm available and reachable 24/7. I have high experience in helping students with their assignments, proposals, and dissertations. Most importantly, I'm a professional accountant and I can handle all kinds of accounting and finance problems.
4.40+
15+ Reviews
45+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra 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...
-
When you drink it remember what it symbolises for you.
-
Consider a one-period, three-state economy with two assets traded. Asset 1 has a price of 0.9 and pays a dividend of 1 no matter what state is realized. Asset 2 has a price of 2 and pays 1, 2, and 4...
-
Jen suspects that Brad is having an affair with Angie, and wants to divorce him. Her prenuptial agreement specifies that if she files for divorce, she receives $60,000, but that her award will double...
-
Assembling a product is an example of a: Multiple Choice Facility-level activity Batch-level activity Unit-level activity O Product-level activity Data concerning three of Kilmon Corporation's...
-
NPV and Discount Rates An investment has an installed cost of $724,860. The cash flows over the four-year life of the investment are projected to be $324,186, $375,085, $354,302, and $205,680. If the...
-
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.
-
What is a purchase-money security interest, and why is it given special priority?
-
31. What is meant by path? 32. Give the formula for calculating D4 and D8 distance. 33. What is geometric transformation? 34. What is image translation and scaling? 35. Define the term Luminance
-
1. Explain Brightness adaptation and Discrimination 2.Explain sampling and quantization:
-
3. Explain about Mach band effect? 4. Explain color image fundamentals. 5. Explain CMY model.
-
1. Describe the fundamental steps in image processing? 2. Explain the basic Elements of digital image processing:
-
3. Explain the Structure of the Human eye 4. Explain the RGB model
-
What force is exerted on the water in an MHD drive utilizing a 25.0-cm-diameter tube, if 100-A current is passed across the tube that is perpendicular to a 2.00-T magnetic field? (The relatively...
-
For a nonzero constant a, find the intercepts of the graph of (x 2 + y 2 ) 2 = a 2 (x 2 - y 2 ). Then test for symmetry with respect to the x-axis, the y-axis, and the origin.
-
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.
-
Just work out the assignment on your own sheet, you dont need the excel worksheet. Classic Coffee Company Best friends, Nathan and Cody, decided to start their own business which would bring great...
-
Financial information related to the proprietorship of Ebony Interiors for February and March 2019 is as follows: February 29, 2019 March 31, 2019 Accounts payable $310,000 $400,000 Accounts...
-
(b) The directors of Maureen Company are considering two mutually exclusive investment projects. Both projects concern the purchase of a new plant. The following data are available for each project...
Study smarter with the SolutionInn App