THE RANKS OF L-FUZZY REGULAR MATRICES AND INVERTIBLE MATRICES

Let A be a matrix over a bounded distributive lattice L.The relations among the row rank r 1(A) ,column rank r 2(A) and Schein rank r(A) of the matrix A are discussed.The Necessary and sufficient conditions for r(A)=1 are obtained,and some methods that can simplify the matrix and preserve the Schein rank are given.It is also proved that r(A)=r 1(A)=r 2(A) for a regular matrix A and r(A)=n for a invertible matrix A over L.