the column rank of is less than or equal to , there exist columns of size such that every column of is a linear combination of , there exist an matrix and a matrix such that (when is the rank, this is a rank factorization of ), there exist rows of size such that every row of is a linear combination of , the row rank of is less than or equal to .
the column rank of is less than or equal to  there exist columns of size such that every column of is a linear combination of  there exist an matrix and a matrix such that (when is the rank, this is a rank factorizatio,n of ) there exist ro,ws of size such that every row ,of is a linear combination of , the row rank of is less than or equal to .