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关于正行列式的一个公开问题 被引量：5

An open problem on positive determinant
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摘要 探讨了非负整半环上矩阵的正行列式,获得了正行列式的重要性质,部分解决了Pop lin与Hartw ig提出的一个公开问题. In this paper, the positive determinant over a nonnegative commutative entire semiring is studied, some important properties of the positive determinant are obtained and an open problem posed by Poplin and Hartwig is partly solved.
作者 谢源 谭宜家
机构地区 福建农林大学金山学院 福州大学数学与计算机科学学院
出处 《福州大学学报（自然科学版）》 CAS CSCD 北大核心 2009年第3期305-307,共3页 Journal of Fuzhou University(Natural Science Edition)
基金 福建省自然科学基金资助项目(Z0511012)
关键词 非负半环 矩阵 正行列式 nonnegative semiring matrix positive determinant
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献3

  • 1Golan J S.Semirings and their applications[M].New York:Kluwer Academic Publishers,1999.
  • 2Poplin P L,Hartwig R E.Determinantal identities over commutative semirings[J].Linear Algebra and its Appl,2004(387):99-132.
  • 3谢源,谭宜家.非负半环上的积和式半群[J].福州大学学报（自然科学版）,2007,35(1):1-5. 被引量：1

二级参考文献5

  • 1Golan J S.Semirings and their applications[M].[s.l.]:Kluwer Academic Publishers,1999.
  • 2Beasley LeRoy B,Cummings L.Permanent semigroups[J].Linear and Multilinear Algebra,1978,5:297-302.
  • 3Poplin P L,Hartwig R E.Determinantal identities over commutative semirings[J].Linear Algebra and Its Application,2004(387):99-132.
  • 4Brualdi R A,Parter S V,Schneider H.The diagonal equivalence of a nonngative matrix to a stochastic matrix[J].J Math Anal Appl,1966,16:31-51.
  • 5Berman A,Plemmons R J.Nonnegative matrices in the mathematical science[M].New York:Academic Press,1979.

同被引文献32

  • 1C. K. LI, N. K. TSING. Linear preserver problems. A brief introduction and some special techniques[J]. Linear Algebra Appl, 1992,162-164.217-235.
  • 2S. W. LIU, D. B. ZHAO. Introduction to Linear Preserver Problems[M]. Harbin.. Harbin Press, 1997:1-23.
  • 3C. K. LI, S. PIERCE. Linear preserver problems[J]. America Mathematical Mothly, 2001,108: 591-605.
  • 4VEIN R. , DALE P.. Determinants and their applications in mathematical physics[M]. New York: Springer- Verlag Press, 1999:99-112.
  • 5GOLAN J. S.. Semirings and Their Aplications, Updated and Expanded Version of the Theory of Semirings, with Applications to Mathematics and Theoretical Computer Science[M]. Dordrecht: Kluwer Academic Publishers, 1999:352-361.
  • 6POPLIN PHILLIP, HARTWIG ROBERT. Determinantal identities over commutative semirings[J]. Linear algebra and its applications, 2004,384 : 99-132.
  • 7BEASLEY LEROY, GUTERMAN ALEXANDER, LEE SANG-GU, et al. Frobenius and dieudonne theorems over semirings[J]. Linear and multilinear algebra, 2007,55(1) : 19-34.
  • 8LI C K, PIERCE S. Linear Preserver Problems [ J]. America Mathematical Monthly, 2001, 108:591 -605.
  • 9DOLINAR G, SEMRL P. Determinant Preserving Maps on Matrix Algebras [J]. Linear Algebra Appl. , 2002, 348: 189- 192.
  • 10TAN V, WANG F. On Determinant Preserver Problems [ J]. Linear Algebra Appl. , 2003, 369:311 -317.

引证文献5

二级引证文献2

福州大学学报（自然科学版）
2009年 第3期

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