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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

Linear Function Linear Equation Single Point Linear Transformation Linear Algebra 
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.

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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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