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对称双随机矩阵逆特征值问题 被引量：1

On the inverse eigenvalue problem for symmetric doubly stochastic matrices
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摘要 研究一种特殊的非负矩阵(对称随机矩阵)逆特征值问题,即对给定的实n-重Λ={λ1,…,λn},求在什么条件下存在的以Λ的谱的对称随机矩阵问题. In the present paper, we studied a special nonnegative inverse eigenvalue problem -- the symmetric doubly stochastic inverse eigenvalue problem which asks for necessary and sufficient conditions on a given n-tuple A = { A l ,＇＂, A n I of real numbers in order that it be the spectrum of a symmetric doubly stochastic matrix.
作者 杨尚俊
机构地区 安徽大学数学科学学院
出处 《安徽大学学报（自然科学版）》 CAS 北大核心 2013年第6期1-7,共7页 Journal of Anhui University(Natural Science Edition)
基金 安徽大学创新团队基金资助项目(KJTD001B)
关键词 逆特征值问题 对称双随机矩阵逆特征值问题 特殊正交矩阵 置换相似 inverse eigenvalue problem symmetric doubly stochastic inverse eigenvalue problem typical orthogonal matrix permutation similar.
分类号 O151 [理学—基础数学]
  • 相关文献

参考文献13

  • 1Borobia A. On the nonegative eigenvalue problem [ J ]. Linear Algebra Appl, 1995 (223/224) : 131-140.
  • 2Fiedler M. Eigenvalues of nonnegative symmetri cmatrices [ J ]. Linear Algebra Appl, 1974 (9) : 119-142.
  • 3Fang M. A note on the inverse eigenvalue problem for symmetric doubly stochastic matrices [ J ]. Linear Algebra App1,2010,d32:2925-2927.
  • 4Horn R A, Johnson C R. Matrix Analysis [ M ]. London: Cambridge University Press, 1985.
  • 5Hwang S G, Pyo S S. The inverse eigenvalue problem for symmetric doubly stochastic matrices [ J ]. Linear Algebra App1,2004 ( 379 ) :77-83.
  • 6Kaddoural C, Mourad B. On a conjecture concerning the inverse eigenvalue problem of 4 ~ 4 symmetric doubly stochastic matrices [ C ]. International Mathematical Forum, 2008,131 ( 3 ) : 1513-1519.
  • 7Mourad B. On a spectrum property of doubly stochastic matrices and its applications to their inverse eigenvalue problem[J]. Linear Algebra Appl,2012(435) :3400-3412.
  • 8Reams R. An inequality for nonnegative matrices and the inverse eigenvalue problem[ J]. Linear Algebra Appl, 1996 (41) :267 -375.
  • 9Satzmann L F. A note on eigenvalues of nonnegative matrices [ J ]. Linear Algebra Appl, 1972 (16) :329-338.
  • 10Soto R, Rojo O. Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem [ J ]. Linear Algebra Appl,2006 (416) :844-856.

二级参考文献15

  • 1Borobia A. On the nonnegative eigenvalue problem [ J ]. Linear Algebra Appl, 1995 ( 223/224 ) : 131 - 140.
  • 2Fang M. A note on the inverse eigenvalue problem for symmetric doubly stochastic matrices [ J ]. Linear Algebra and Appl, 2010,432:2925-2927.
  • 3Horn R A, Johnson C R. Matrix analysis[ M ]. London: Cambridge University Press, 1985.
  • 4Hwang S G, Pyo S S. The inverse eigenvalue problem tbr symmetric doubly stochastic matrices [ J ]. Linear and Algebra Appl,2004,379:77-83.
  • 5Kaddoural C, Mourad B. On a conjecture concerning the inverse eigenvalue problem of 4×4 symmetric doubly stochastic matrices [ J ]. International Mathematical Forum ,2008,131 ( 3 ) : 1513-1519.
  • 6Kelog R B. Matrices similar to a positive or esencially positive matrix[ J ]. Linear Algebra and Appl, 1971,4:191-204.
  • 7Laffey T J, Meehan E. A characterization of trace zero nonnegative 5×5 matrices[ J ]. Linear Algebra and Appl, 1999,302 : 295 -302.
  • 8Lowey R, London D. A note on an inverse problem for nonnegative matrices[ J]. Linear and Muhilinear Algebra, 1978 (6) :83-90.
  • 9Nazari A M, Sherafat F. On the inverse eigenvalue problem for nonnegative matrices of order two to five [ J ]. Linear Algebra and Appl,2012,436 : 1771 - 1790.
  • 10Perfect H, Mirsky L. Spectral properties of doubly stochastic matrices [ J ]. Monatsh Math, 1965,69:35-57.

共引文献1

同被引文献11

  • 1Borobia A.On the nonegative eigenvalue problem[J].Linear Algebra Appl,1995,223:131-140.
  • 2Fiedler M.Eigenvalues of nonnegative symmetricmatrices[J].Linear Algebra Appl,1974,9:119-142.
  • 3Hwang S G,Pyo S S.The inverse eigenvalue problem for symmetric doubly stochastic matrices[J].Linear Algebra Appl,2004,379:77-83.
  • 4Kaddoural C,Mourad B.On a conjecture concerning the inverse eigenvalue problem of 4×4 symmetric doubly stochastic matrices[J].International Mathematical Forum,2008,31(3):1513-1519.
  • 5Mourad B.On a spectrum property of doubly stochastic matrices and its applications to their inverse eigenvalue problem[J].Linear Algebra Appl,2012,435:3400-3412.
  • 6Reams R.An inequality for nonnegative matrices and the inverse eigenvalue problem[J].Linear Algebra Appl,1996,41:267-375.
  • 7Satzman F L.A note on eigenvalues of nonnegative matrices[J].Linear Algebra Appl,1972,41:329-338.
  • 8Soto R,Rojo O.Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem[J].Linear Algebra Appl,2006,416:844-856.
  • 9Yang S,Li X.Inverse eigenvalue problems of 4×4 irreducible nonnegative matrices[C]∥Advances in Matrix Theory and Applications,the proceedings of the Eighth International Conference on Matrix Theory and Applications,World Academic Union,2008.
  • 10Yang S,Xu C.Row stochastic inverse eigenvalue problem[J].Journal of Inequalities and Applications,2011(24):1-5.

引证文献1

安徽大学学报（自然科学版）
2013年 第6期

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