×

Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

12

0

24

Class Note for MATH 322 with Professor Glickenstein at UA

Marketplace > University of Arizona > Class Note for MATH 322 with Professor Glickenstein at UA

No professor available

These notes were just uploaded, and will be ready to view shortly.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
24
WORDS
KARMA
25 ?

Popular in Department

This 24 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 12 views.

×

Reviews for Class Note for MATH 322 with Professor Glickenstein at UA

×

×

What is Karma?

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15
w d 2 5 u 5 kpm g A paw rm Q 2 3 3 Eigenvalues and eigenvectors 0 Let A be a square n X n matrix We say that X is an eigenvector of A with eigenvalue A if X 34E 0 and AX AX o The above equation can be re written as A 7 AInX 0 0 Since X 7E 0 this implies that A iAlr is not invertible ie that detA 7 AI 0 o The eigenvalues of A are therefore found by solving the characteristic equation detA 7 AI 0 Eigenvalues o The characteristic polynomial detA iAln is a polynomial of degree n in A It has n complex roots which are not necessarily distinct from one another 0 If A is a root of order k of the characteristic polynomial detA 7 AI we say that A is an eigenvalue of A of algebraic multiplicity k 0 If A has real entries then its characteristic polynomial has real coefficients As a consequence if A is an eigenvalue of A so is A o It A is a 2 X 2 matrix then its characteristic polynomial is of the form A2 7 ATrA detA where the trace of A TrA is the sum of the diagonal entries of A Ei genvectors 0 Once an eigenvalue A of A has been found one can find an associated eigenvector by solving the linear system AiAInX0 0 Since NA iAln is not trivial there is an infinite number of solutions to the above equation In particular if X is an eigenvector of A with eigenvalue A so is XX where X 6 R or C and 0c 7E 0 o The set of eigenvectors of A with eigenvalue A together with the zero vector form a subspace of R or C EA called the eigenspace of A corresponding to the eigenvalue A o The dimension of E is called the geometric multiplicity of A Eigenvectors continued 0 Examples Find the eigenvectors of the following matrices Each time give the algebraic and geometric multiplicities of the corresponding eigenvalues 7 710 0A70 5

×

25 Karma

×

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Janice Dongeun University of Washington

"I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!
×

Refund Policy

STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com