CAJ | 학술논문

Z-矩阵是很重要的一类特殊矩阵,近年来线性代数及其应用领域的众多研究者都对此类矩阵作过深入的研究,发表了大量的文章.著名矩阵论学者R.S.Smith最近在世界数学核心刊物:<线性代数及其应用>38卷中发表了一篇重要文章(见参考文献[1]).该文对于一般的Z-矩阵给出很好的变换刻画.特别给出各重要矩阵类Lk,k=1,2,...,n的刻画(n为矩阵的阶).我们发现R.S.Smith的文章中存在一些问题,甚至可能是错误.本文就是针对这些问题进行讨论,包括对文章的某些部分进行了一些改进.
Z-구진시흔중요적일류특수구진,근년래선성대수급기응용영역적음다연구자도대차류구진작과심입적연구,발표료대량적문장.저명구진론학자R.S.Smith최근재세계수학핵심간물:<선성대수급기응용>38권중발표료일편중요문장(견삼고문헌[1]).해문대우일반적Z-구진급출흔호적변환각화.특별급출각중요구진류Lk,k=1,2,...,n적각화(n위구진적계).아문발현R.S.Smith적문장중존재일사문제,심지가능시착오.본문취시침대저사문제진행토론,포괄대문장적모사부분진행료일사개진.
Z-matrices are important special matrices that attract attentions of many researches working in area of Linear Algebra and its Applications. R.L. Smith's paper[1] published recently on Linear Algebra and Its Applications Vol.338(2001) is a very interesting paper. His paper gave a very nice transformational characterization for the Z-matrices in general as well as for each of the important classes of Lk ,k=1,...,n, where n is the order of the Z-matrices. We found in the paper some problems and some are possible errors. Here we try to give possible improvements for all the errors we have found.