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矩阵方程AXB+CYD=E的对角称(英文) 被引量：4

SYMMETRIC SOLUTIONS OF THE MATRIX EQUATION AXB+CYD=E
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摘要 本文讨论了方程AXB+CYD=E的矩阵极小范数对称解.利用矩阵的Kronecker积与广义逆给出了解存在的充分必要条件及解的表达式. In this paper,the symmetric solution with minimum-norm of the matrix equation AXB+CYD=E is considered.A necessary and sufficient condition for the existence of the symmetric solution and the expression of such solution are given by using the Kronecker product and the generalized inverses.
作者 蒋家尚 袁永新
机构地区 江苏科技大学数学系
出处 《南京大学学报（数学半年刊）》 CAS 2008年第2期141-148,共8页 Journal of Nanjing University(Mathematical Biquarterly)
关键词 矩阵方程 对称解 极小范数 广义逆 matrix equation symmetric solution minimum-norm generalized inverses
分类号 O151.21 [理学—基础数学]
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参考文献10

  • 1Aubin J P.Applied Functional Analysis. . 1979
  • 2BAKSALARY J K,KALA R.The matrix equation AXB + C YD = E. Linear Algebra and Its Applications . 1980
  • 3Ben-Israel A,,Greville T N E.Generalized Inverses: Theory and Applications. . 1974
  • 4Chang X W,,Wang J S.The Symmetric solution of matrix equationsAX+YA=C,AXAT+BYBT=C,and(ATXA,BTXB)=(C,D). Linear Algebra and Its Applications . 1993
  • 5King-Wah,Eric Chu.Singular value and generalized singular value decompositions andthe solution of Linear matrix equations. Linear Algebra and Its Applications . 1987
  • 6Mirko Dobovisek.On minimal solutions of the matirx equation AX-YB = 0. Linear Algebra and Its Applications . 2001
  • 7Jameson A,Kreindler E,Lancaster P.Symmetric positive semidefinite and positive definite real solutions of AX = XATand AX = YB. Linear Algebra and Its Applications . 1992
  • 8Liao,A. P.,Bai,Z. Z.,Lei,Y.Best approximate solution of matrix equation AXB + CY D = E. SIAM Journal on Matrix Analysis and Applications . 2005
  • 9Shim S Y,Chen Y.Least squares solutions of matrix equation AXB~*+CYD~*=E~*. SIAM Journal on Matrix Analysis and Applications . 2003
  • 10Xu G P,Wei M S and Zheng D S.On solutions of matrix equation AXB+CYD = F. Linear Algebra and Its Applications . 1998

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南京大学学报（数学半年刊）
2008年 第2期

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