Prove that any quadratic form can be written as where A, are the eigenvalues of A and Icirc cedil i (x, vi) denotes the angle between x and the ith eigenvector ( , cos 0 Ax x'...

Prove that any quadratic form can be written as where A, are the eigenvalues of A and

Question:

Prove that any quadratic form can be written as

where A, are the eigenvalues of A and Î¸i = Š€(x, vi) denotes the angle between x and the ith eigenvector.

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

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 09:08 AM

See More Questions

(a) Prove that any square matrix A can be written as the sum of a symmetric matrix and a skew symmetric matrix. (b) Illustrate pact (a) for the matrix 369 258 147
a. Show that if A is an n n matrix, then where i , . . . , n are the eigenvalues of A. b. Show that A is singular if and only if = 0 is an eigenvalue of A. det AT.
Exercise 32 in Section 4.3 demonstrates that every polynomial is (plus or minus) the characteristic polynomial of its own companion matrix. Therefore, the roots of a polynomial p are the eigenvalues...
A bartender employed in a licensed establishment over-serves a patron. As a result of the over-service, the patron physically assaults another patron by striking him with a beer bottle. Identify and...
Simons credit-card limit has been reached. He owes more than $10,000. Titan Credit Corp., the creditor, refuses to extend the time for payment. Using his extensive knowledge of software code, Simon...
On 1 August 2006 X Ltd granted a 20-year lease to Y Ltd on the following terms: An annual rental of 20,000, payable quarterly in advance on 1 August, 1 November, 1 February and 1 May each year. A...
Studies of Asian (particularly Japanese) and U.S. managers in the 1970s and 1980s found sharp differences of opinion and attitude toward quality management. Do these differences continue to'exis;? To...
1. Use the FOLKLORE method to complete the documentation of the Management Information Systems Unit GEMS system. Be sure to include customs, tales, sayings, and art forms. 2. In two paragraphs,...
Cari and Jenny adopt a Korean orphan. The adoption takes 2 years and two trips to Korea and is finalized in 2020. They pay $7,000 in 2019 and $7,500 in 2020 for qualified adoption expenses. In 2020,...
Understand the process of mobile manufacturing company commencing from raw material decision to final delivery to the end consumer. Make a flow chart and suggest a strategy for procurement, vendor...
True or false: A matrix with a real orthonormal eigenvector basis is symmetric.
An elastic body has stress tensor Find the principal stretches and principal directions of stretch. 2-3 131 312
Who are some contemporary leaders that you would identify as charismatic? Think about individuals in the nonprofit sector, business, and government. How do they exhibit the behaviors of charismatic...
1) Why do you believe that in recent years PE sponsors have increasingly chosen to buy debt in their distressed LBOs? 2) What are the pros and cons of this investment strategy? 3) What issues are...
Paper Street Soap Company Ltd conducts a business that makes luxury soaps. It operates a factory in Oyster Bay near Sydney. The factory contains a large amount of equipment that is used in the...
TRANSACTION ANALYSIS: Dartmouth Ties Corporation is a merchandising company that has been in operation for two years. The company sell high - end ties for men. They purchase their inventory from...
Using your knowledge of types of group influence and of subcultures, explain the potential impact on consumer behavior of Methodism's tightening of its ban on gay marriage and LGBTA clergy. Write in...
A language L over an alphabet is co-finite, if * \ Lis empty or finite. Let COFNFA = {(N) | N is a NFA accepting a co-finite language}. Show that COF NFA is decidable.
When the original poverty line was created, not everyone who was in poverty had access to a phone or running water in their homes. What are some things you think are necessary to enjoy a reasonable...
According during to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1,088 in 2018. Consider the population of "last-minute" filers who mail...
Refer to the data in Exercise 11-10 on y = wear volume of mild steel and x = oil viscosity. Find a 95% confidence interval on each of the following: (a) Intercept (b) Slope (c) Mean wear when oil...
Exercise 11-11 presented data on chloride concentration y and roadway area x on watersheds in central Rhode Island. Find a 99% confidence interval on each of the following: (a) B1 (b) B0 (c) Mean...
Refer to the data in Exercise 11-12 on rocket motor shear strength y and propellant age x. Find a 95% confidence interval on each of the following: (a) Slope B1 (b) Intercept B0 (c) Mean shear...
Each week you must submit an annotated bibliography. Entries of current events relating to the economic concepts and the impact on the company or the industry of your company. You must use acceptable...
Fluffy Toys Ltd produces stuffed toys and provided you with the following information for the month ended August 2020 Opening WIP Units 5,393 units Units Started and Completed 24,731 units Closing...
Part A Equipment 1,035,328 is incorrect Installation 44,672 is incorrect Anything boxed in red is incorrect sents 043/1 Question 9 View Policies Show Attempt History Current Attempt in Progress...

Prove that any quadratic form can be written as where A, are the eigenvalues of A and

Question:

(Σ || > À, cos? 0; Ax = || x'

Step by Step Answer:

Using the spectral factori...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions