Advertisement

# Linear Transformations and Matrices

• Thomas Banchoff
• John Wermer
Part of the Undergraduate Texts in Mathematics book series (UTM)

## Abstract

In Chapter 4.1 we examined a number of transformations T of 4-space all of which have the property that the coordinates of T(X) are given as linear functions of the coordinates of X. In each case we have formulas of the sort
$$T\left( {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}}\\ {{x_4}} \end{array}} \right)\;{\rm{ = }}\;\left( {\begin{array}{*{20}{c}} {{a_{11}}{x_1}\; + \;{a_{12}}{x_2}\;{\rm{ + }}\;{a_{13}}{x_3}\;{\rm{ + }}\;{a_{14}}{x_4}}\\ {{a_{21}}{x_1}\; + \;{a_{22}}{x_2}\;{\rm{ + }}\;{a_{23}}{x_3}\;{\rm{ + }}\;{a_{24}}{x_4}}\\ {{a_{31}}{x_1}\; + \;{a_{32}}{x_2}\;{\rm{ + }}\;{a_{33}}{x_3}\;{\rm{ + }}\;{a_{34}}{x_4}}\\ {{a_{41}}{x_1}\; + \;{a_{42}}{x_2}\;{\rm{ + }}\;{a_{43}}{x_3}\;{\rm{ + }}\;{a_{44}}{x_4}} \end{array}} \right).$$

## Keywords

Linear Function Linear Transformation Linear Algebra Matrix Theory Crucial Property
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Springer-Verlag New York, Inc. 1992

## Authors and Affiliations

• Thomas Banchoff
• 1
• John Wermer
• 1
1. 1.Department of MathematicsBrown UniversityProvidenceUSA