P3 [Discovery proof of SVD for a 2 2 matrix] Let A a) Verify that the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
P3 [Discovery proof of SVD for a 2 2 matrix] Let A a) Verify that the vectors vi [cos 0 sin 0 and v2 = [-] sin 0 cos 0 are orthonormal for any choice of the parameter 0 <0 < 2. b) (MATLAB) Plot the angle between Av and Av as a function of 0. For how many angles are Avi and Av2 orthogonal? c) Show that Av, and Av are orthogonal if and only if tan 20 = 3. How many angles exist in the interval [0, 2) satisfying this condition? Explain why this corresponds to choosing {v1, v2}. d) (MATLAB) For all the angles obtained in c) numerically determine ||Av ||2 and ||Av2||2. e) Assume that tan 20 = 3. Show that = ||Avi ||2||Av2||2 = 02 provided cos 20 > 0. f) Assume tan 20 = with cos 20 0 and let u Av2. Explain why = = Avi, uz U = = [u | u], = | 0 002] and V = [p| v2] provide a SVD decomposition A = UV of A. g) (MATLAB) Numerically compare the decomposition obtained in f) with the results of the MATLAB function svd for the two angles 0 satisfying tan 20 = with cos 20 0. P3 [Discovery proof of SVD for a 2 2 matrix] Let A a) Verify that the vectors vi [cos 0 sin 0 and v2 = [-] sin 0 cos 0 are orthonormal for any choice of the parameter 0 <0 < 2. b) (MATLAB) Plot the angle between Av and Av as a function of 0. For how many angles are Avi and Av2 orthogonal? c) Show that Av, and Av are orthogonal if and only if tan 20 = 3. How many angles exist in the interval [0, 2) satisfying this condition? Explain why this corresponds to choosing {v1, v2}. d) (MATLAB) For all the angles obtained in c) numerically determine ||Av ||2 and ||Av2||2. e) Assume that tan 20 = 3. Show that = ||Avi ||2||Av2||2 = 02 provided cos 20 > 0. f) Assume tan 20 = with cos 20 0 and let u Av2. Explain why = = Avi, uz U = = [u | u], = | 0 002] and V = [p| v2] provide a SVD decomposition A = UV of A. g) (MATLAB) Numerically compare the decomposition obtained in f) with the results of the MATLAB function svd for the two angles 0 satisfying tan 20 = with cos 20 0.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these programming questions
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Q1. You have identified a market opportunity for home media players that would cater for older members of the population. Many older people have difficulty in understanding the operating principles...
-
Communication: What are the characteristics of effective communication relevant to your team project submission? Relate to theory. Provide a minimum of 4. ( 8 ) Assess your communication...
-
The file MarketPenetration contains the market penetration value (the percentage of the country population that are users) for the 15 countries that lead the world in total number of Facebook users:...
-
The following transactions affected various funds and activities of the Town of Big Springs. 1. The Fire Department, a governmental activity accounted for within the General Fund, purchased $100,000...
-
Comparing current and prior year revenues and expenses and investigating all changes exceeding 10 percent would most likely reveal that: a. Management's capitalization policy for small tools changed...
-
The income statement of Mazor Company is presented here. Additional information:1. Accounts receivable decreased $380,000 during the year, and inventory decreased $300,000.2. Prepaid expenses...
-
Write a program in C# Sharp to read 10 numbers from keyboard and find their sum and average Hint: use for loop Sample Output: I/P: 2, 4, 6, 8, 10, 12, O/P: Sum is 110 Avg is 11 20
-
Record the following petty cash transactions of Lexite Laminated Surfaces in general journal form (explanations are not required): Apr. 1 Established a petty cash fund with a $200 balance. 30 The...
-
Determine at least one (1) strategy and one (1) process on how these responsibilities must be fulfilled. Briefly describe any additional information you need to communicate information about the work...
-
The equation of motion of a particle is given in Cartesian coordinates by the relation \(\mathbf{r}(t)=\alpha t^{2} \hat{\mathbf{i}}+\beta t^{2} \hat{\mathbf{j}}\). Determine (i) the trajectory of...
-
The original 1966 version of this taut drama about a plane crash and efforts of survivors to literally rebuild their damaged plane into a smaller flying machine to escape their plight in the desert...
-
An AMAZON pack of mass \(7.0 \mathrm{~kg}\) is stationary on a horizontal rough surface. The coefficient of static friction for the pack is \(\mu_{s}=0.85\). The pack sorting device acts with a force...
-
Now choose one of the organizations from Exercise 20 and visit it on different social platforms. What does the company do to engage customers? Write a short report to the VP of marketing to identify...
-
Evaluate the limits in Problems 3-7. \(\lim _{n ightarrow \infty}(2 n+3)\)
-
Determine the appropriate classification in the fair value hierarchy for each of the instruments referenced in the case as of December 31, 2016. Provide support from appropriate authoritative...
-
An 8.0 kg crate is pulled 5.0 m up a 30 incline by a rope angled 18 above the incline. The tension in the rope is 120 N, and the crates coefficient of kinetic friction on the incline is 0.25. a. How...
-
Identify which of the following sets are compact and which are not. If E is not compact, find the smallest compact set H (if there is one) such that E H. a) {1/k : k N)U{0} b) {(x, y) R2: a < x2 +...
-
Prove that (1 - x/k)k e-x uniformly on any closed, bounded subset of R.
-
Use Exercise 10.7.1 to prove that if f C[a, b] and For k = 0, 1,..., then f(x) = 0 for all x [a, b). Ja f(x) xk dx = 0
-
Fill in the blank: If two variables have a positive association, then large values of one variable are associated with __________________ values of the other.
-
Percentiles are values that divide a data set into hundredths. The values that divide a data set into tenths are called deciles, denoted D1,D2, ...,D9. Describe the relationship between percentiles...
-
For each of the following pairs of variables, determine whether the association is positive or negative, and explain why. a. Would the association between outdoor temperature and consumption of...
Study smarter with the SolutionInn App