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arXiv · 1009.1768

Invertible Symmetric 3 x 3 Binary Matrices and GQ(2,4)

Andrea Blunck·Peter Levay·Metod Saniga·Peter Vrana
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Abstract

We reveal an intriguing connection between the set of 27 (disregarding the identity) invertible symmetric 3 x 3 matrices over GF(2) and the points of the generalized quadrangle GQ(2,4). The 15 matrices with eigenvalue one correspond to a copy of the subquadrangle GQ(2,2), whereas the 12 matrices without eigenvalues have their geometric counterpart in the associated double-six. The fine details of this correspondence, including the precise algebraic meaning/analogue of collinearity, are furnished by employing the representation of GQ(2,4) as a quadric in PG(5,2) of projective index one. An interesting physical application of our findings is also mentioned.

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Andrea Blunck, Peter Levay, Metod Saniga, Peter Vrana. 2010-09-09. Invertible Symmetric 3 x 3 Binary Matrices and GQ(2,4). https://doi.org/10.1080/03081087.2011.651725

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