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# Symmetric Matrices

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

## Abstract

In the 2-dimensional case, we saw that a special role is played by matrices $$\left( {\begin{array}{*{20}{c}} a&b\\ b&d \end{array}} \right)$$ which have both off-diagonal elements equal. The corresponding condition in 3 dimensions is symmetry about the diagonal. We say that a matrix is symmetric if the entry in the ith position in the jth column is the same as the entry in the jth position in the ith column, i.e., a ij = a ji for all i,j,
$$\left( {\begin{array}{*{20}{c}} a&b&c\\ b&d&e\\ c&e&f \end{array}} \right)\; = \;\left( {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}}&{{a_{13}}}\\ {{a_{12}}}&{{a_{22}}}&{{a_{23}}}\\ {{a_{13}}}&{{a_{23}}}&{{a_{33}}} \end{array}} \right).$$
(1)

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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