review3_2009_10_09

review3_2009_10_09 - 1 EE263 Review session 3 Jong-Han Kim...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 EE263 Review session 3 Jong-Han Kim 2009.10.09. EE263 Review session 3 • Eigenvalues / eigenvectors • Symmetric matrices • Quadratic forms • Positive definiteness • Examples 2 EE263 Review session 3 Jong-Han Kim 2009.10.09. Eigenvalues and eigenvectors For A ∈ R n × n , there exists nonzero v ∈ C n such that Av = λv any such v is called an eigenvector of A associated with eigenvalue λ how to compute • ( λI − A ) has nonzero null space, thus det ( λI − A ) = 0 which is a polynomial of order n • the following matlab command finds eigenvectors and eigenvalues [V D] = eig(A); 3 EE263 Review session 3 Jong-Han Kim 2009.10.09. examples • consider A = bracketleftbigg 1 2 2 1 bracketrightbigg • λ makes ( λI − A ) rank deficient, ⇒ λ 1 = 3 and λ 2 = − 1 • v ∈ null ( λI − A ) , ⇒ v 1 = [1 1] T and v 2 = [1 − 1] T • what if A is rank-deficient already? for example, A = bracketleftbigg 1 2 2 4 bracketrightbigg 4 EE263 Review session 3 Jong-Han Kim 2009.10.09. examples • what are the eigenvalues of A = 1 2 3 0 4 5 0 0 6 ? • what are the eigenvalues of A = 1 0 0 0 2 0 0 0 3 ? • what are the eigenvalues of A = 1 0 5 2 4 9 3 3 1 5 0 0 4 0 0 0 0 5 7 0 0 0 9 8 2 ? 5 EE263 Review session 3 Jong-Han Kim 2009.10.09....
View Full Document

This note was uploaded on 08/23/2010 for the course EE 263 taught by Professor Boyd,s during the Fall '08 term at Stanford.

Page1 / 15

review3_2009_10_09 - 1 EE263 Review session 3 Jong-Han Kim...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online