Lecture Notes 11

# Lecture Notes 11 - Lecture11 1 October 11, 2007 Outline: 1)...

This preview shows pages 1–3. 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: Lecture11 1 October 11, 2007 Outline: 1) Quick Review of the Big Picture of the 4 subspaces 2) The picture for a Full Column rank matrix 3) Motivation for Projections (The small picture) 4) Projection onto a line 5) Projection onto a subspace and the "normal equations" A T Ax =A T b Lecture 11: Projections ^ Orthogonality of the 4 subspaces: The Big (Strangian) Picture Point: For every matrix A there are 4 fundamental subspaces Two in R n : Two in R m: The Big Picture of Ax =b Full Column Rank: Point: For every matrix A there are 4 fundamental subspaces Two in R n : Two in R m: The Small Picture of a Full Column rank problem: Motivation for Projections and "Least-Squares Problems" Lecture11 2 October 11, 2007 Projection onto a Line: (1-dim subspace) Projection onto a Line: (1-dim subspace) Steps: 1) find the "least squares solution" x 2) find the projection p 3) find the Projection Matrix P ^ Projection onto a Line: (1-dim subspace) Example: Project b =[ 1 1 1]' onto the line spanned by a...
View Full Document

## This note was uploaded on 06/02/2010 for the course APMA APMA E3101 taught by Professor Spiegelman during the Fall '07 term at Columbia.

### Page1 / 4

Lecture Notes 11 - Lecture11 1 October 11, 2007 Outline: 1)...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online