By means of the associated digraph of matrices we obtain the necessary and sufficient conditions of whether irreducibly doubly diagonally dominant matrices belongs to non - singular m - matrices 借助于矩陣的伴隨有向圖得到了不可約雙對(duì)角占優(yōu)矩陣是否為非奇異m -矩陣的充分必要條件。
And meantime a - doubly diagonally dominant matrices was studied in detail . the paper points out that as long as we examine the related quantity involved in the circuit of the associated digraph of matrices we may determine whether a matrix is a non - singular m - matrices or not 同時(shí)詳細(xì)研究了-雙對(duì)角占優(yōu)矩陣,指出只要對(duì)矩陣伴隨有向圖圈中所涉及到的相關(guān)量進(jìn)行驗(yàn)證即能判別一個(gè)矩陣是否為非奇異m -矩陣。
Based on the results , chapter 3 obtains the necessary and sufficient conditions of the positive line a - doubly diagonally dominant matrices being non - singular m - matrices , by means of the nature of the associated digraph of matrices irreducible and weakly irreducible matrices . the results obtained simplify the process of judgment , only making us to check the related quantity involved in the circuit of the associate digraph of matrices 第三章在已有結(jié)果的基礎(chǔ)上,借助于矩陣的伴隨有向圖、不可約以及弱不可約矩陣的性質(zhì),得到了正線-雙對(duì)角占優(yōu)矩陣為非奇異m -矩陣的充分必要條件,所獲結(jié)果簡(jiǎn)化了判定過(guò)程,只需要對(duì)矩陣伴隨有向圖圈中所涉及到的相關(guān)量進(jìn)行驗(yàn)證即可。