The e value is 1 1 0 since sh 1 0 2 ii sc 10

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: re multiples of x = 1 0 . The e-value is λ = 1. 1 0 , since Sh 1 0 = 2 (ii) Sc = 10 04 y scale y (1, 4) −→ 1 1 (1, 1) x 1 x Multiples of x1 = λ2 = 4. (iii) P = y 1 0 , x2 = 0 1 , e-values λ1 = 1, 10 00 projection y (1, 1) −→ x x 1 1 1 Multiples of x1 = multiples of x2 = 0 1 1 0 since P x1 = x1 , λ1 = 1 and since P x2 = 0 · x2, λ2 = 0. 3 (iv) Re = 2c2 − 1 2cs 2cs 2s − 1 2 for θ = π/4, 01 10 so c = s = √ 2/2 and Re = . y y 1 −→ θ 1 x 1 x 1 Multiples of x1 = and x2 = 1 −1 1 1 since Re 1 −1 1 1 = 1 −1 1 1 , λ1 = 1 since Re = −1 , λ2 = −1. 4 (v) Ro = s c −s c y y −→ θ x x no e-vector unless θ = π Ro = x1 x2 −1 0 0 −1 e-vector: any vector x = , e-value λ = −1. 5...
View Full Document

This note was uploaded on 04/09/2011 for the course MATH 232 taught by Professor Russel during the Spring '10 term at Simon Fraser.

Ask a homework question - tutors are online