If A is an n n positive definite matrix and U is an n m

Question:

If A is an n × n positive definite matrix and U is an n × m matrix of rank m, show that UTAU is positive definite.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra With Applications

ISBN: 9780070985100

7th Edition

Authors: W. Keith Nicholson

See More Books

Question Posted: Jun 21, 2016 06:47 AM

See More Questions

Let A be a symmetric positive definite matrix and let Q be an orthogonal diagonalizing matrix. Use the factorization A = QDQT to find a nonsingular matrix B such that BTB = A.
Let A be an n n symmetric positive definite matrix. For each x, y Rn, define (x, y) = xTAy Show that ( , ) defines an inner product on Rn.
An n x n symmetric matrix A is positive semi definite if xT Ax 0 for all x in Rn. Prove the following: (a) Every positive definite matrix is positive semi definite. (b) If A is singular and positive...
Single PlantwideandMultiple Production Department Factory Overhead Rate Methodsand Product Cost Distortion The management of Nova Industries Inc. manufactures gasoline and diesel engines through two...
Jones, CPA, has completed the audit of Sarack Lumber Supply Co. and has issued a standard unqualified report. In addition to a report on the overall financial statements, the company needs a special...
Define fixed and variable costs and give examples of each in manufacturing. What is total cost, and what is the equation for it?
What approach should Hoi take to getting bills paid from delinquent customers? LO.1
Able Control Company, which manufactures electrical switches, uses a standard cost system and carries all inventory at standard cost. The standard factory overhead cost per switch is based on direct...
Gaston finds a book in the middle of the street Gaston must leave the book at the nearest police station so the true owner May return and recover the book true or false
The Kinder Institute at Rice University in Houston has surveyed people in the Houston area for several decades on a multitude of issues. An explanation of the research, along with a codebook for the...
If A and B are positive definite and r > 0, show that A + B and rA are both positive definite. If A and B are positive definite, show that
In each case find the QR-factorization of A. (a) (b) 1011 1101
Outline practical syntheses of each of the following compounds from benzene, alcohols, and any necessary organic or inorganic reagents: (a) 1-Chloro-2-phenylethane
I Need Hr project on Employee Engagement What is Employee Engagement and how does it contribute to organizational success? What is the role of HR in improving employee engagement? What are some...
In the United States, the Veterans Administration (VA) is tasked with, among other things, providing quality health care for U.S. military veterans. Chronically underfunded, the agency was having...
Using the keywords you brainstormed earlier in the module, conduct three separate searches in CQ Researcher - SAGE, Academic Search Ultimate, or another relevant database. When conducting these...
TechEx Repair allows local hardware stores to expand their service offerings to their customers by providing an off-site small engine repair service. Customers bring in small engines such as lawn...
Purpose: Sometimes we are asked to collaborate with a team of writers. This collaboration can help us to understand how others think differently from us and help us to think more creatively. This...
If 21 g of H 2 S is mixed with 38 g of O 2 and 31 g of SO 2 forms, what is the percentage yield? 2 HS + 3 O 2 SO + 2 HO
The following table shows the rates of total return in successive years from 2004 to 2008 for the Sprott Canadian Equity Fund and for the benchmark Toronto Stock Exchange S&P/TSX Composite Index. By...
Find the point of intersection of the line of intersection of the given planes. (a) 2x + 3y - 4z + 5 = 0 and -3x + 2y + 5z + 6 = 0 (b) 3x - 2y - 5z + 4 = 0 and 2x + 3y + 4z + 8 = 0.
(a) Show that the graph of an equation of the form given in (10), with a, b, and c not all zero, is a plane with normal v = ai + bj + ck. (b) Show that the set of all points on the plane ax + by + cz...
Let u = u1i + u2j + u3k, 3k, v = v1i + v2j + u3k, and w = w1i + w2j + w3k be vectors in P3. Show that
The following information is provided by Garden Gears for a new product it recently introduced: Total unit cost $50 Desired ROI per unit $22 Target selling price $72 How much is Garden Gears'...
Solid bank loan P5 million to a borrower on January 1, 2018. The terms of the loan require principal payments of P1 million each year for five years plus interest at 8%. The first principal and...
3) Assuming annual sales of $250,000 and a 50% gross (contribution) margin, calculate the following a. Average collection period if ending receivables total $45,000 b. Ending days-on-hand of...

If A is an n n positive definite matrix and U is an n m

Question:

Step by Step Answer:

Given x in R n x T U T AUx Ux T A Ux 0 provided ...View the full answer

Linear Algebra With Applications

Students also viewed these Linear Algebra questions