# Sol-HW7 - Math Methods Solutions for Assignment 7 Oct 18...

This preview shows pages 1–2. Sign up to view the full content.

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

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

Unformatted text preview: Math Methods Solutions for Assignment 7 Oct. 18, 2010 Fall 2010 Linear Spaces, Linear Operators Due Oct. 25, 2010 1 (5). For the vectors in three dimensions, ~ v 1 = ˆ x + ˆ y, ~ v 2 = ˆ y + ˆ z, ~ v 3 = ˆ z + ˆ x use the Gram-Schmidt procedure to construct an orthonormal basis starting from ~ v 1 . ~e 1 = ~v 1 || v 1 || = ˆ x + ˆ y √ 2 ~u 2 = ~v 2- < ~e 1 | ~v 2 > ~e 1 ; < ~e 1 | ~v 2 > = 1 √ 2 ; ~u 2 = ˆ y + ˆ z- 1 √ 2 ˆ x + ˆ y √ 2 =- 1 2 ˆ x + 1 2 ˆ y + ˆ z ~e 2 = ~u 2 || u 2 || =- 1 2 ˆ x + 1 2 ˆ y + ˆ z q 1 4 + 1 4 + 1 =- 1 √ 6 ˆ x + 1 √ 6 ˆ y + r 2 3 ˆ z ~u 3 = ~v 3- < ~e 1 | ~v 3 > ~e 1- < ~e 2 | ~v 3 > ~e 2 ; < ~e 1 | ~v 3 > = 1 √ 2 ; < ~e 2 | ~v 3 > =- 1 √ 6 + r 2 3 = 1 √ 6 ~u 3 = ˆ z + ˆ x- ˆ x + ˆ y 2 + 1 6 ˆ x- 1 6 ˆ y- 1 3 ˆ z = 2 3 ˆ x- 2 3 ˆ y + 2 3 ˆ z = 2 3 (ˆ x- ˆ y + ˆ z ) ~e 3 = ~u 3 || u 3 || = 2 3 (ˆ x- ˆ y + ˆ z ) q 3 · 4 9 = ˆ x- ˆ y + ˆ z √ 3 2 (10). For the vector space of polynomials in x , use the scalar product defined as...
View Full Document

## This note was uploaded on 09/28/2011 for the course PHYSICS 801 taught by Professor Ivanov during the Fall '10 term at Kansas State University.

### Page1 / 3

Sol-HW7 - Math Methods Solutions for Assignment 7 Oct 18...

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

View Full Document
Ask a homework question - tutors are online