賈明輝，韓貴春

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*賈明輝，韓貴春

(內(nèi)蒙古民族大學(xué)數(shù)學(xué)學(xué)院，內(nèi)蒙古，通遼 028000)

0 前言

1 記號(hào)與定義

顯然，不可約矩陣是弱不可約矩陣的特殊形式。

在接下來的討論中，引入下列符號(hào)：

則為非奇異-矩陣。

引理2.5設(shè)＝(a) ∈C×n∩，若∈2(α)，則為非奇異-矩陣。

又由引理2.1知，為非奇異-矩陣。

即

故有

即

即(1) 式成立。

則

綜上，由引理2.2知為非奇異-矩陣。

則為非奇異-矩陣。

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*JIA Ming-hui, HAN Gui-chun

(School of Mathematics, Inner Mongolia University for the Nationalities, Tongliao, Inner Mongolia 028000, China)

The concept of weakly irreducible2- diagonally dominant matrices according to circuit is introduced. Firstly, an equivalent condition for judging weakly irreducible strictly2- diagonally dominant matrices according to circuit is given. Furthermore, some new practical criteria for nonsingular-matrices are obtained for the theory of diagonally dominant matrices. The study enriches and perfects the theory of- diagonally dominant matrices according to circuit and nonsingular H-matrices.

1674-8085(2018)01-0012-05

O151.21

A

10.3969/j.issn.1674-8085.2018.01.003

2017-09-04；

2017-11-12

內(nèi)蒙古自治區(qū)自然科學(xué)基金項(xiàng)目(2016MS0118)；內(nèi)蒙古民族大學(xué)科學(xué)研究基金項(xiàng)目(NMDYB1778，NMDYB15089)

*賈明輝(1977-)，女，內(nèi)蒙古呼倫貝爾人，副教授，主要從事數(shù)值代數(shù)與矩陣?yán)碚摲矫娴难芯?E-Mail:47398255@qq.com);韓貴春(1978-)，女，山東陽谷人，講師，博士生，主要從事數(shù)值代數(shù)與矩陣?yán)碚摲矫娴难芯?E-mail:380973379@qq.com).