Rank of convex combinations of matrices

摘要

LetAandBbe complex rectangular matrices of the same rankr. We characterize the property that all convex combinations ofAandBare of rankr. Moreover, forAandBof full rank, some conditions for the matrix setr(A, B) (c(A, B), resp.) whose rows (columns, resp.) are independent convex combinations of the rows (columns, resp.) ofAandBare also proposed.