If {v 1 ,v 2 ,.........v n } is an orthonormal basis for R n and A
Question:
If {v1,v2,.........vn} is an orthonormal basis for Rn and
A = c1v1vT1 + c2v2vT2 +..........+ cnvnvTn
Prove that A is a symmetric matrix with eigenvalues c1, c2,......cn and corresponding eigenvectors v1, v2,......., vn.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 57% (7 reviews)
Since v 1 v 2 v n is an orthonormal basis we have Since w...View the full answer
Answered By
Carly Cimino
As a tutor, my focus is to help communicate and break down difficult concepts in a way that allows students greater accessibility and comprehension to their course material. I love helping others develop a sense of personal confidence and curiosity, and I'm looking forward to the chance to interact and work with you professionally and better your academic grades.
4.30+
12+ Reviews
21+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics 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 units of an item available for sale during the year were as follows: There are 57 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the...
-
How important are sales transactions in the typical audit engagement?
-
Casio Company uses a predetermined rate for applying overhead costs to production. The rates for Year 0 follow: variable, $1 per unit; fixed, $2 per unit. Actual overhead costs incurred follow:...
-
Conduct a SWOT analysis of Starbucks (3 in each of the 4 sections of SWOT). Based on your analysis suggest three strategies they could pursue to more firmly establish their competitive position.
-
Fifteen percent of Australians smoke. By introducing tough laws banning brand labels on cigarette packages, Australia hopes to reduce the percentage of people smoking to 10% by 2018 (Reuters website,...
-
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...
-
Swinson, Inc., a private company that applies ASPE, incurred $15,000 in materials and $12,000 in direct labour costs between January and March 2014 to develop a new product. In May 2014, the criteria...
-
The order entry system will allow a 10 percent variation in list price. For example, an item with a list price of \($1\) could be sold for 90 cents or \($1.10\) without any system interference. The...
-
Explain throttling calorimeter.
-
The project team has just started planning as a result of the charter being signed. Of the following, which does the charter not provide? a. Defines the scope statement b. Outlines the project...
-
Define laws of thermodynamics.
-
The inventory item number was omitted on the purchase order. Which control will detect this error?
-
In problem, determine the quadratic function whose graph is given. 4 Vertex: (2, 3) 2 5 -1 1 3 (0, 1)
-
What are the risks and liability factors in an audit? What are the implications to the auditor? What are the implications to the organization? How can the auditor mitigate these risks and liability...
-
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...
-
The market price of a security is $50. Its expected rate of return is 10%. The risk-free rate is 5%, and the market risk premium is 8%. What will the market price of the security be if its beta...
-
At the end of 2025, Aramis Company has accounts receivable of $800,000 and an allowance for doubtful accounts of $40,000. On January 16, 2026, Aramis Company determined that its receivable from...
-
Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the...
Study smarter with the SolutionInn App