Linear Transformations and Matrices

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

Abstract

In Chapter 3.1 we examined a number of transformations T of 3-space, all of which have the property that in terms of the coordinates of \( X = \left( {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right), \) the coordinates of T(X) are given by linear functions of these coordinates. In each case the formulae are of the following type:
$$ T\left( {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {{a_1}{x_1}\;{\rm{ + }}\;{a_2}{x_2}\;{\rm{ + }}\;{a_3}{x_3}}\\ {{b_1}{x_1}\;{\rm{ + }}\;{b_2}{x_2}\;{\rm{ + }}\;{b_3}{x_3}}\\ {{c_1}{x_1}\;{\rm{ + }}\;{c_2}{x_2}\;{\rm{ + }}\;{c_3}{x_3}} \end{array}} \right). $$

Keywords

Dinates 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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