Explain why the singular values of A are the same as the nonzero eigenvalues of the positive
Question:
Explain why the singular values of A are the same as the nonzero eigenvalues of the positive definite square root matrix S = √ATA , defined in Exercise 8.5.27.
Data From Exercise 8.5.27
(a) Prove that every positive definite matrix K has a unique positive definite square root, i.e., a matrix B > 0 satisfying B2 = K.(b) Find the positive definite square roots of the following matrices:
(i)
(ii)
(iii)
(iv)
Transcribed Image Text:
21 12
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 57% (7 reviews)
The singular values of A are the positive square roots of the eigenvalues of ATA Let the eigenvalu...View the full answer
Answered By
Collins Njuguna
I graduated from Maseno University with a Bachelor of Science in Applied Statistics. After graduation, I started tutoring students in mathematics. My experience in mathematics education is extensive and varied. I have taught a wide range of topics, including algebra, geometry, trigonometry, calculus, statistics, probability, and computer science. I have also worked with students of all ages and backgrounds, from elementary school to college.
My teaching method is based on the idea of hands-on learning. I believe that students learn best when they are actively engaged in the learning process, so I focus on giving students the tools they need to explore the material on their own. I also emphasize the importance of practice and review, as these are essential for mastering math concepts.
I have also developed several online and in-person courses on mathematics. My courses are designed to help students learn mathematics in an efficient and comprehensive way, and I use a variety of activities and exercises to ensure that my students are engaged and motivated.
Overall, my passion for mathematics and teaching has allowed me to be a successful tutor and educator in the field. I am confident that my experience will help your students master the mathematics they need to succeed.
0.00
0 Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Prove that, if A is a symmetric matrix with eigenvalues 1, 2,..., n, then the singular values of A are |1|, |2|,..., |n|.
-
(a) Prove that every positive definite matrix K has a unique positive definite square root, i.e., a matrix B > 0 satisfying B2 = K. (b) Find the positive definite square roots of the following...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Calculate the new profit sharing ratio after the admission of Fischer. Assignment Ubisoft Entertainment is a partnership of exclusive game distributors who specialize in electronic arts and play...
-
Give two examples of business-specific risks that could have a negative effect on a valuation estimate.
-
A steel containing 0.95% C is heated to various temperatures above the eutectoid temperature, held for 1 h, and then quenched to room temperature. Using Figure 12-32, determine the amount and...
-
The current market interest rate on U-Store City Investment Building bonds is $10 \%$, compounded semiannually. The original bonds are sold as $\$ 1,000,12 \%$ interest rate notes. A batch of bonds...
-
The following is taken from the Colaw Company balance sheet. Interest is payable annually on January 1. The bonds are callable on any annual interest date. Colaw uses straight-line amortization for...
-
Before recording adjusting entries on December 31, the Store Supplies account had a $1,900 debit balance, while a physical count of the supplies showed $300 of unused supplies on hand. Prepare the...
-
Hard Core had budgeted sales of 190,000 feet of its concrete culvert products for June 2010. Each foot of product requires 4 pounds of concrete ($0.10 per pound) and 7.5 pounds of gravel ($0.04 per...
-
Write down (a) A 2 2 matrix that has 0 as one of its eigenvalues and (1, 2) T as a corresponding eigenvector; (b) A 3 3 matrix that has (1, 2, 3) T as an eigenvector for the eigenvalue 1.
-
Show that one can compute the variance of a set of measurements without reference to the mean by the following formula 2 x 2m = m m * i=1 j=1 (-x) = #2 - ) (-x;). m
-
A flywheel with a radius of 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.600 rad/s2, compute the magnitude of the tangential acceleration, the radial...
-
the answer Warren proposes a tax on the monetary lobbying efforts and contributions of corporations and interest groups to limit their influence. Why is this unlikely to completely limit the role of...
-
The report must consist of headings such as Accounts Receivable and Inventory (topics from the textbook); other examples would be Income Statement, Balance Sheet, and the Statement of Shareholders'...
-
Select all that apply What two benefits are associated with companies' effort to increase social responsibility?
-
How can tags be used to manage costs in Azure?
-
what is the answer Warren proposes a tax on the monetary lobbying efforts and contributions of corporations and interest groups to limit their influence. Why is this unlikely to completely limit the...
-
Janet (who has made no taxable gifts) is considering transferring assets valued at $9 million to an irrevocable trust (yet to be created) for the benefit of her son, Gordon, age 15, with Farmers Bank...
-
On 1 July 2021, Croydon Ltd leased ten excavators for five years from Machines4U Ltd. The excavators are expected to have an economic life of 6 years, after which time they will have an expected...
-
(a) Prove that where a = -tan 1/2 θ and b = sin θ. (b) Is the factorization valid for all values of θ? (c) Interpret the factorization geometrically. cos sin...
-
(a) Find the matrix in R3 that corresponds to a counterclockwise rotation around the x-axis through an angle 60. (b) Write it as a product of elementary matrices, and interpret each of the factors.
-
Determine the matrix representative for orthogonal projection P: R2 R2 on the line through the origin in the direction (a) (1, 0)T (b) (1, 1)T (c) (2, -3)T
-
Kariong Manufacturing an Australian manufacturing company is importing car parts from Thailand and currently the exchange rate is AUD/THB 31.37. Kariong has just signed a contract with its Thailand...
-
Diamond Machine Technology has invested $250,000 in developing a sharpener. Each sharpener costs $3 to make. In addition, fixed costs for the sharpener are $10,000. The company expects to sell...
-
Bullish Forecast You are a Wall Street Microsoft analyst looking to make a name for yourself as a Microsoft Bull. Implement a growth and profitability outlook greater than the Credit Suisse analyst....
Study smarter with the SolutionInn App