• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.115-122
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• 2004

We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. Let $S_{n}(F)$ be the space of all $n\;\times\;n$ symmetry matrices over a field F with 2, $3\;\in\;F^{*}$, then T is an additive injective operator preserving rank-additivity on $S_{n}(F)$ if and only if there exists an invertible matrix $U\;\in\;M_n(F)$ and an injective field homomorphism $\phi$ of F to itself such that $T(X)\;=\;cUX{\phi}U^{T},\;\forallX\;=\;(x_{ij)\;\in\;S_n(F)$ where $c\;\in;F^{*},\;X^{\phi}\;=\;(\phi(x_{ij}))$. As applications, we determine the additive operators preserving minus-order on $S_{n}(F)$ over the field F.