Rank comparisons Original Research Article

The column rank of an m × n matrix B with entries in A is the dimension of its column space, and the factor rank of B is the smallest integer k such that B = XY for some m × k and k × n matrices X and Y with entries in A. We consider matrices whose entries can be viewed as elements of different, but related, algebraic systems. We investigate how the column rank and the factor rank change as the algebraic system changes.