This preview shows page 1. Sign up to view the full content.
Unformatted text preview: E for more details. When a linear mapping is dened in some way other than giving the coordinate polynomials, there is an easy way to nd its matrix representative. The proof of the following is outlined in Exercise 3 : Remark 4.1.1. The j th column of the matrix representative [ L ] of a linear mapping L : R 3 R 3 is the coordinate column of L ( e j ) , where { e 1 , e 2 , e 3 } are the standard basis vectors for R 3 . 2 To avoid tortuous constructions or notations, we will work here with mappings of space to space; the analogues when the domain or target (or both) lives in the plane or on the line are straightforward....
View Full
Document
 Spring '08
 ALL
 Calculus, Transformations

Click to edit the document details