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Determinants

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

Abstract

Let m be the matrix
$$ \left( {\begin{array}{*{20}{c}} {{a_1}}&{{a_2}}&{{a_3}}\\ {{b_1}}&{{b_2}}&{{b_3}}\\ {{c_1}}&{{c_2}}&{{c_3}} \end{array}} \right). $$
Let A, B, C denote the row vectors of this matrix. The quantity
$$ A\;\cdot\;{\rm{(}}B\;{\rm{x}}\;C{\rm{)}}\;{\rm{ = }}\;B\;\cdot\;(C\;{\rm{x}}\;A)\;{\rm{ = }}\;C\;\cdot\;(A\;{\rm{x}}\;B) $$
is called the determinant of m and is denoted det(m) or
$$ \left| {\begin{array}{*{20}{c}} {{a_1}}&{{a_2}}&{{a_3}}\\ {{b_1}}&{{b_2}}&{{b_3}}\\ {{c_1}}&{{c_2}}&{{c_3}} \end{array}} \right|. $$

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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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