If v 1 ,v 2 , v n is an orthonormal basis for R n and A c 1 v 1 v T 1 c 2 v 2 v T 2 c n v n v T n Prove that A is a symmetric matrix with eigenvalues c 1 , c 2 , c n and corresponding eigenvectors v 1 , v 2 , , v n ...

Since v 1 v 2 v n is an orthonormal basis we have Since w ...

If {v 1 ,v 2 ,.........v n } is an orthonormal basis for R n and A

Question:

If {v₁,v₂,.........v_n} is an orthonormal basis for Rⁿ and

A = c₁v₁v^T₁ + c₂v₂v^T₂ +..........+ c_nv_nv^T_n
Prove that A is a symmetric matrix with eigenvalues c₁, c₂,......c_n and corresponding eigenvectors v₁, v₂,......., v_n.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-0538735452

3rd edition

Authors: David Poole

See More Books

Question Posted: Nov 14, 2018 04:18 AM

See More Questions

Let U be an m-dimensional subspace of Rn and let V be a k-dimensional subspace of U, where 0 < k < m. (a) Show that any orthonormal basis (v1, v2,...,vk} for V can be expanded to form an orthonormal...
Let u be a vector in an inner product space V, and let (v1, v2, ..., vn) be an orthonormal basis for V. Show that if a1 is the angle between u and vi then Cos2a1 + cos22 + . . . + cos2an = 1
Let (u1. u2, . . . , un), be an orthonornial basis for Rn and let A be a linear combination of the rank I matrices u1uT1.u2uT2..... unun. If how that A is a symmetric matrix with eigenvalues c1,c2...
Given the following table of assets held at death, how much is the probate estate worth? Asset Value (millions) Notes Investments $7 Retirement Account $6 Named Beneficiary Residence $4 Joint Tenancy...
What types of formal and informal groups would you expect to find in a racing team? What roles could each play in helping the team toward a winning season?
The in situ moist unit weight of a soil is 17.3 kN/m3 and the moisture content is 16%. The specific gravity of soil solids is 2.72. This soil is to be excavated and transported to a construction site...
A statistician is designing a phase III clinical trial comparing a continuous outcome in two groups receiving experimental versus standard therapy with a total sample size of 168 patients. The team...
Santana Rey, owner of Business solutions, decides to diversify her business by also manufacturing computer workstation furniture. Required 1. Classify the following manufacturing costs of Business...
The computer workstation furniture manufacturing that Santana Rey started is progressing well. As of the end of June, Business Solutions's job cost sheets show the following total costs accumulated...
The matching principle requires: That bad debt expenses be reported in the same accounting period as the sales they helped generate and requires the use of the alowance method of accounting for bad...
Let (a) Orthogonally diagonalize A. (b) Give the spectral decomposition of A. 2 1 -1 A = -1 2
Prove Theorem 5.24. Let A be an n n symmetric matrix. The quadratic form f (x) x T Ax is a. positive definite if and only if all of the eigenvalues of A are positive. b. positive semidefinite if...
Draw Newman projections for the anti and gauche conformations about the C C bond of these compounds. What other factors, besides steric and tor-sional strain, influence the stability of these...
Assume that two business owners A and B each own an identical storage building valued at $8000. Assume there is a 30% chance in any year that each building will be destroyed by a peril, and that a...
You are a bond analyst working for a hedge fund. A bond you follow has face value 100, has a coupon rate of 5% (paid once a year) and matures in 5 years. You are trying to find if there is any...
Use the information below to answer questions 7 to 10. Below is the balance sheet of Lagenda Sdn. Bhd for the years 2019 and 2020. 2020 Note RM'000 2019 RM'000 Note 2020 RM000 2019 RM'000 ASSETS...
A project is estimated to complete in 6 months. Refer to the table below. The total budgeted cost is $ till completion of the whole project. The cumulative budgeted cost is $ at the end of month 4....
In a PowerPoint presentation, provide the following slides Cover Page (in speaker notes, provide an introduction of the purpose of the presentation). Product and Price: Choose an existing product or...
Assume that the universe has an edge. Placing yourself at that edge in a thought experiment, explain why this assumption violates the cosmological principle.
1. Advertising for eyeglasses _________ (increases/decreases) the price of eyeglasses because advertising promotes _________. 2. An advertisement that succeeds in getting consumers to try the product...
Provide 95% confidence limits for each of your estimates?
What is the best-fitting regression line relating mean thyroxine level to gestational age? Pediatrics, Endocrinology Transient hypothyroxinemia, a common finding in premature infants, is not thought...
Answer the same questions posed in Problem 11.47 for IQF? Data from 11.47 LD72 and LD73 are variable names for the actual blood-lead levels in 1972 and 1973, respectively. Use regression methods to...
Sales quantity Sales Direct material Direct labor Manufacturing overhead Selling and Admin. Expenses The total cost of goods sold is 1,000 $66.00 per unit $12.00 $4.00 $3.00 per unit $1,800 per month...
Let R denote the region in the xy-plane that lies in the first quadrant and is bounded by the lines y = 1 - x, y = 2 - x, y = x + 1, and y = x - 1. Set u=x+y and v = y-x. (a) Solve for x and y in...
Reply to The culture established by Mr. Kelleher places importance on employee happiness, which directly influences customer satisfaction and overall organizational achievements. To maintain this...

If {v 1 ,v 2 ,.........v n } is an orthonormal basis for R n and A

Question:

Step by Step Answer:

Since v 1 v 2 v n is an orthonormal basis we have Since w...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Mathematics questions