rec4 - EE 221 : Linear Systems Recitation #4 Sam Burden Sep...

Info iconThis preview shows pages 1–2. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EE 221 : Linear Systems Recitation #4 Sam Burden Sep 17, 2010 1 Continuity & Linearity Revisited Fact L p ( I ) := f : I R | R I | f | p < is a (pseudo-)metric space with d ( f,g ) := (R I | f- g | p ) 1 /p . Exercise Consider A : ( L p ([0 , 1]) ,d ) ( R , || ) defined by A ( f ) := f (1). (a) Is A linear? Yes: A ( a ( f + g )) = a A ( f ) + a A ( g ). (b) Is A continuous? No: x n 0, but (1) n = 1 for all n . Eigenstructure Definition C is an eigenvalue of A C n n if there is an eigenvector v 6 = 0 : Av = v . Definition The spectrum of A is the set of eigenvalues, denoted spec A . Exercise Suppose for A : ( F n ,F ) ( F n ,F ) there is F and a basis { b j } n j =1 for which A b 1 = b 1 and A b k = b k + b k- 1 for k = 2 ,...,n . Find the matrix representation of A . Induced Norm Let A : ( U,F, || U ) ( V,F, || V ) be linear....
View Full Document

Page1 / 2

rec4 - EE 221 : Linear Systems Recitation #4 Sam Burden Sep...

This preview shows document pages 1 - 2. Sign up to view the full document.

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