Let {u 1 ..........u n } be an orthonormal basis for R n , and let
Question:
Let {u1..........un} be an orthonormal basis for Rn, and let λ1..........λn be any real scalars. Define A = λ1u1u1T+.............+ λnununT
a. Show that A is symmetric.
b. Show that λ1,..........λn are the eigenvalues of A.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 75% (4 reviews)
a To show that A is symmetric we need to show that A equals its transpose The transpose of A is give...View the full answer
Answered By
Mary Boke
I have teached the student upto class 12th as well as my fellow mates.I have a good command in engineering,maths and science.I scored 90+ marks in 10th and 12th in maths.
0.00
0 Reviews
10+ Question Solved
Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
Question Posted:
Students also viewed these Mathematics questions
-
Let B = {e1, e2,..., en} be an orthonormal basis of an inner product space V. Given T: V V, define T': V V by (a) Show that (aT)' = aT'. (b) Show that (5 + T)' = S' + T' (c) Show that MB(T') is the...
-
Let S = {v1, v2,..., vk} be an orthonormal basis for the Euclidean space V and {a1, a2,..., ak) be any set of scalars none of which is zero. Prove that T = {a1v1,a2v2, ...,akvk} is an orthogonal...
-
Let u1, ...,uk be an orthonormal basis for the subspace W Rm. Let A = (u1, u2 ... uk) be the m à k matrix whose columns are the orthonormal basis vectors, and define P = AAT to be the...
-
A research laboratory receives delivery of a new custom-made cylindrical thin-wall pressure vessel. The pressure vessel has inner radius R = 300 mm, and wall thickness t = 10 mm. The vessel is made...
-
Bell Incorporated (BI) purchased a group of assets together from one of their competitors whose owner had recently decided to retire and stop operations. BI paid $ 500,000 for land, building,...
-
Explain how IBM can use a forward rate agreement to lock in the cost of a one-year $25 million loan to be taken out in six months. Alternatively, explain how IBM can lock in the interest rate on this...
-
a. What purpose is served by management letters? b. List the types of data that may be included in management letters?
-
Cereal Cheaters (CCACC) suspects that cereal companies, including Oxford Cereals, are cheating consumers by packaging cereals at less than labeled weights. Recently, the group investigated the...
-
The Caf Food and Beverage Expenses Essendon includes: 75% of expenses related to food 25% of expenses related to beverages. To calculate the portion of expenses related to food, multiply the total...
-
Find (a) The maximum value of Q(x) subject to the constraint x T x = 1, (b) A unit vector u where this maximum is attained, and (c) The maximum of Q(x) subject to the constraints x T x = 1 and x T u...
-
Let A be an n x n symmetric matrix of rank r. Explain why the spectral decomposition of A represents A as the sum of r rank 1 matrices.
-
Explain how a business can ensure that their employees are not involved in any illegal or other inappropriate activity with respect to computers, the internet, and voice mail.
-
How can FSAs and HSAs be used to manage health-related costs?
-
Value at Risk (VaR) and Expected Shortfall (ES) are two measures of market risk employed by financial institutions and their regulators. a) VaR calculation is based on daily earning at risk (DEAR)....
-
Twin Oaks Brewery (TOB) needs to borrow $20 million immediately. It can borrow for three years at a fixed rate of 7.5% or at a floating rate of LIBOR + 40 basis points. Plain vanilla...
-
The current price of UCD Inc. is $15 per share; put options and call options on the stock both have a strike price of $15 and are selling for $0.75 per option. Suppose on the expiration date the...
-
A bank reports the following items on its latest balance sheet: allowance for loan and lease losses $52 million; undivided profits $62 million; subordinated debt capital $8 million; common stock and...
-
For each lettered part, a through c, examine the two given sets of numbers. Without doing any calculations, decide which set has the larger standard deviation and explain why. Then check by finding...
-
A consumer magazine is evaluating five brands of trash compactors for their effectiveness in reducing the volume of typical household products that are discarded. In the experiment, each block...
-
Often research articles include tables of comparisons for demographics of experimental groups. In one such article (Psycho-Oncology, 2006) reporting a study investigating the effect of art therapy on...
-
How good are you at estimating how many calories you expend? Researchers Harris et al. (American Journal of Mens Health, 2010) conducted a study where 80 males (ages 2145 years) were first given a...
-
Refer to the previous exercise about the study of the relationship between dietary restraint and energy expenditure. Another response variable the researchers were interested in was the estimation of...
-
Determine the gcd of the following pairs of polynomials. a. (x3 + 1) and (x2+x+1) over GF(2)
-
(a) Consider a particle at position r = (x, y, z) spinning around the axis u where u = angular velocity w. The motion of the particle is given by the equation dr (wu) r dt with initial condition...
-
Describe how change management practices can influence the success or failure of organizational change initiatives. What are the key factors that contribute to employee resistance to change, and what...
Study smarter with the SolutionInn App