诣零矩阵和拟阵

Nil-Matrices and Matroid

对于一个包含关系的关联矩阵,文献[1]构造了一个拟阵,并由关联矩阵定义了诣零矩阵(nil-矩阵),而且讨论了它的相关性质,进而提出具有N-特征的矩阵(即nil-矩阵)能否构造一个拟阵.本文在文献[2～5]的基础上,通过反例证明nil-矩阵不一定能构造拟阵,又给出了一个较强的能构造拟阵的nil-矩阵的条件,即对于关联矩阵A,若任意秩为的子矩阵皆为nil-矩阵,则(D,N(A))是一个拟阵,且其秩为,而且这个矩阵A的所有nil-矩阵都是拟阵(D,N(A))的独立集.

For a relation with the incidence matrix, the paper [ 1 ] has raised a question,i, e. can we construct a matroid by the matrix with N-property （nil-matrix）？ Based on the answer of the question by a reverse example, it isn＇ t fixed. In the same time, it gives a stronger condition of nil-matrix that can construct a matroid as follows. For incidence matrices A, if they are nil-matrix in which the arbitrary submatrices orders are r^-, （D,N,（A）） they are matoid. If their order is ？, all of the A＇s nil-matrices is the gathering independently of the matoid （D,N,（A） ）.