Necessary and Sufficient Condition for the Equality Sign in Inequality about Rank of Sum of Matrix
Suya Sun · Harbin Ligong Daxue xuebao · 2011
There are inequalities about rank of the sum of two matrices in advanced algebra.However,few people study the problems of inequality about rank of sum of some matrices and the conditions for equality sign in the inequality.In this paper,we firstly discuss the inequalities about rank of sum of a number of matrices.Secondly,by mathematical induction and partition of the matrix we give the condition to hold the identity in the above inequality,i.e.the rank of the sum of matrix equal to the sum of their rank if and only if they can be transformed synchronously into block diagonal matrix.Finally,we give its applications for two matrices in linear algebra.