线性代数中一类分块矩阵的极小秩

Minimal Rank of a Class of Partitioned Matrices in Linear Algebra

对于数域F,若A∈F^(m1×n1),B∈F^(m1×n2),C∈F^(m2×n1),X取F^(m2×n2)中任意矩阵,构造出分块矩阵■.对该分块矩阵的极小秩问题进行讨论,并给出了该分块矩阵极小秩的表达式,同时给出了满足条件的矩阵X的表达式.

For the number field,if A∈F^(m1×n1),B∈F^(m1×n2),C∈Fm2×n1,X is any matrice inF^(m2×n2),the partitioned matrices ■.In this paper,the minimum rank of the partitioned matrices is discussed;its expression and the expression of the matrix X which satisfies the condition are given.