title: Tan's Epsilon-Determinant and Ranks of Matrices over Semirings.
abstract: We use the ϵ-determinant introduced by Ya-Jia Tan to define a family of ranks of matrices over certain semirings. We show that these ranks generalize some known rank functions over semirings such as the determinantal rank. We also show that this family of ranks satisfies the rank-sum and Sylvester inequalities. We classify all bijective linear maps which preserve these ranks.
authors.affiliation: Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada N1G 2W1.
authors.forename: Preeti
authors.initials: P
authors.lastname: Mohindru
authors.affiliation: Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada N1G 2W1.
authors.forename: Rajesh
authors.initials: R
authors.lastname: Pereira