正则的符号蕴含正交模式(英文)

Regular Sign Potentially Orthogonal Sign Patterns

一对符号模式行(或列)向量是蕴含正交的,若存在一对与它们有相同符号模式的正交实行(或列)向量.一个没有零行或零列的n阶符号模式矩阵是符号蕴含正交的,若每一对行和列向量都是蕴含正交的.本文证明了当n为偶数时,存在k正则n阶符号蕴含正交模式的充分必要条件是1≤k≤n;当n≠5为奇数时,存在k正则n阶符号蕴含正交模式的充分必要条件是1≤k≤n且k≠2 ;当n=5时。

A pair of sign pattern row vectors (respectively, column vectors) allows orthogonality if the two vectors are the sign patterns of two real orthogonal row vectors (respectively, column vectors). A square sign pattern matrix that does not have a zero row or zero column is sign potentially orthogonal (SPO) if every pair of rows and every pair of columns allow orthogonality.