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

sinO 

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

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

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