Completely Positive Matrices Having Cyclic Graphs
图是圈的完全正矩阵(英文)
摘要
We prove that a CP matrix A having cyclic graph has exactly two minimal rank 1 factorization if det M(A) > 0 and has exactly one minimal rank 1 factorization if detM(A) = 0.
本文证明，图是围的完全正矩阵Ａ当比较矩阵Ｍ（Ａ）的行列式大于零时，恰有两个极小秩１分解，而当ｄｅｔＭ（Ａ）＝０时，恰有一个极小秩１分解．
参考文献4
-
1[1]BERMAN A and KOGAN N. Characterization of completely positive graphs [J]. Discrete Mathematics, 1993, 114:297-304.
-
2[2]BERMAN A and PLEMMONS R. Nonnegative Matrices in the Mathematical Science [M].2nd ed., Academic, New York, 1994.
-
3[3]DREW J H, JOHNSON C R and LOEWY R. Completely positive matrices associated with M-matrices [J]. Linear and Multilinear Algebra, 1994, 37: 303-310.
-
4[4]MINC H. Nonnegative Matrices [M]. John Wiley and Sons, New York, 1988.
-
1杜翠真.五阶完全正矩阵的一个充要条件[J].河西学院学报,2016,32(2):25-31.
-
2徐常青.Completely Positive Realizations of a Cycle[J].Journal of Mathematical Research and Exposition,2002,22(3):391-395.
-
3杨凯凡.关于矩阵的Perron根[J].怀化学院学报,2005,24(5):43-44.
-
4李大林.完全正矩阵的Hadamard积分解及其空间分布[J].柳州职业技术学院学报,2001,1(3):65-68.
-
5向淑晃,谭立云.等距同构与完全正矩阵[J].石油大学学报（自然科学版）,2000,24(1):112-113.
-
6徐常青.关于完全正矩阵的几点注记(英文)[J].工科数学,2000,16(3):22-27.
-
7张翔,郝雷,王卿文.矩阵方程组中心对称解的极秩[J].上海大学学报（自然科学版）,2012,18(6):596-600.
-
8孙萍,孟令胜.反序律B｛1,2,i｝A｛1,2,i｝=(AB)｛1,2,i｝i=3,4成立的充要条件[J].兰州理工大学学报,2011,37(3):167-172.
-
9陈嘉佳,谭宜家.关于矩阵空间上保持极小秩的线性算子[J].福州大学学报（自然科学版）,2007,35(1):6-8. 被引量：1
-
10查秀秀,李莹,王方圆.具有特殊结构的最小二乘广义逆[J].聊城大学学报（自然科学版）,2015,28(1):10-14.
