A Study Of The Rank Of A Class Of Special Symbol Matrices

As a vital part of sign pattern matrices,the research on the rank of sign matrix belongs to category of the combinatorial matrix theory.An alternating sign matrix is a square(+1,-1,0)-matrix without zero rows and columns,such that the +1 s and-1 s alternate in each row and column,beginning and ending with a +1.A matrix is said to be dense if there are no zeros between two nonzero entries for every line(row,column)of this matrix.Change the ‘0' element in the sign matrix A to ‘1',and change ‘1' and ‘-1' to ‘0'.In the way,we can obtain a(0,1)-matrix B,and it is called the complement matrix of A.In this thesis,we study a class of special sign matrices——dense alternating sign complement matrices.This thesis gives a comprehensive study for the solving process about its rank.At the beginning of the passage,the research background,related concepts and the progress for the research of sign matrices.The main results of this paper are also introduced.Next,the main research contents of this thesis are given,it including the following parts:In the first part,the solving process of the rank of this matrices is researched.In the second part,when n?5k,we present a calculation algorithm for rank and provide a practical example to verify the feasibility of the algorithm.In the third part,the result of the program implementation of the matrix rank is given.