Matrices that preserve vectors of fixed sign variation

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.

Keywords:

• Sign preservation
• Sign regular matrices
• Total positivity
• Monomial matrix

Keywords:

• AMS Subject Classifications: 15A48
• 15A04

Acknowledgement

This Research is partially supported by the Spanish Research Grant MTM2006-03388, Gobierno de Aragón and Fondo Social Europeo.