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The Matrix Relative to a Given Basis

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

Abstract

In Chapter 3.2 we assigned to each linear transformation T of ℝ3 a matrix m(T) as follows:
$$ \begin{array}{l} If\;\;\;T\left( {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}}\\ {{x_3}} \end{array}} \right)\;{\rm{ = }}\;\left( {\begin{array}{*{20}{c}} {{a_1}{x_1}\;{\rm{ + }}\;{a_2}{x_2}\;{\rm{ + }}\;{a_3}{x_3}}\\ {{b_1}{x_1}\;{\rm{ + }}\;{b_2}{x_2}\;{\rm{ + }}\;{b_3}{x_3}}\\ {{c_1}{x_1}\;{\rm{ + }}\;{c_2}{x_2}\;{\rm{ + }}\;{c_3}{x_3}} \end{array}} \right),\;\;\;{\rm{then}}\\ m(T)\;{\rm{ = }}\;\left( {\begin{array}{*{20}{c}} {{a_1}}&{{a_2}}&{{a_3}}\\ {{b_1}}&{{b_2}}&{{b_3}}\\ {{c_1}}&{{c_2}}&{{c_3}} \end{array}} \right)\;. \end{array} $$

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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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