Abstract
For each k≥ 0, those nonsingular matrices that transform the set of totally nonzero vectors with k sign variations into (respectively, onto) itself are studied. Necessary and sufficient conditions are provided. The cases k=0,1,2,n-3,n-2,n-1 are completely characterized.
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Acknowledgement
This Research is partially supported by the Spanish Research Grant MTM2006-03388, Gobierno de Aragón and Fondo Social Europeo.