Determinants and Quadratic Forms

  • George Pólya
  • Gabor Szegö
Part of the Springer Study Edition book series (SSE)

Abstract

Interchanging two numbers in the numbering of the vertices is equivalent to the simultaneous interchange of two rows and two columns. If we give opposite vertices of the octahedron numbers that differ by 3, then the determinant
$$ \left| {\begin{array}{*{20}c} 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill \\ 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill \\ 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill \\ 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill \\ 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill \\ 1 \hfill & 1 \hfill & 0 \hfill & 1 \hfill & 1 \hfill & 0 \hfill \\ \end{array} } \right| = 0. $$

Keywords

Power Series Quadratic Form Principal Diagonal Opposite Vertex Toeplitz Form 
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 Berlin Heidelberg 1976

Authors and Affiliations

  • George Pólya
    • 1
  • Gabor Szegö
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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