The extremal ranks of A 1 - B 1 X C 1 subject to a pair of matrix equations

Yongge Tian; Yonghui Liu

Rendiconti del Seminario Matematico della Università di Padova (2006)

  • Volume: 116, page 55-69
  • ISSN: 0041-8994

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Tian, Yongge, and Liu, Yonghui. "The extremal ranks of $A_1 - B_1 X C_1$ subject to a pair of matrix equations." Rendiconti del Seminario Matematico della Università di Padova 116 (2006): 55-69. <http://eudml.org/doc/108702>.

@article{Tian2006,
author = {Tian, Yongge, Liu, Yonghui},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {55-69},
publisher = {Seminario Matematico of the University of Padua},
title = {The extremal ranks of $A_1 - B_1 X C_1$ subject to a pair of matrix equations},
url = {http://eudml.org/doc/108702},
volume = {116},
year = {2006},
}

TY - JOUR
AU - Tian, Yongge
AU - Liu, Yonghui
TI - The extremal ranks of $A_1 - B_1 X C_1$ subject to a pair of matrix equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2006
PB - Seminario Matematico of the University of Padua
VL - 116
SP - 55
EP - 69
LA - eng
UR - http://eudml.org/doc/108702
ER -

References

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  2. [2] C. DAVIS, Completing a matrix so as to minimize the rank, Oper. Theory: Adv. Appl. 29 (1988), pp. 87-95. Zbl0646.15001MR945004
  3. [3] C.R. JOHNSON, Matrix completion problems: a survey, In Matrix Theory and Applications, Proc. Sympos. Appl. Math. AMS 40 (1990), pp. 171-197. Zbl0706.15024MR1059486
  4. [4] C.R. JOHNSON, G.T. WHITNEY, Minimum rank completions, Linear and Multilinear Algebra 28 (1991), pp. 271-273. Zbl0775.15001MR1088424
  5. [5] G. MARSAGLIA - G.P.H. STYAN, Equalities and inequalities for ranks of matrices, Linear and Multilinear Algebra 2 (1974), pp. 269-292. Zbl0297.15003MR384840
  6. [6] S.K. MITRA, A pair of simultaneous linear matrix equations A1XB1 = C1 and A2XB2 = C2 and a programming problem, Linear Algebra Appl. 131 (1990), pp. 107-123. Zbl0712.15010MR1057067
  7. [7] A.B. ÖÈZGÜLER - N. AKAR, A common solution to a pair of linear matrix equations over a principal ideal domain, Linear Algebra Appl. 144 (1991), pp. 85-99. Zbl0718.15006MR1081877
  8. [8] Y. TIAN, The solvability of two linear matrix equations, Linear and Multilinear Algebra 48 (2000), pp. 123-147. Zbl0970.15005MR1813440
  9. [9] Y. TIAN, Completing block matrices with maximal and minimal ranks, Linear Algebra Appl. 321 (2000), pp. 327-345. Zbl0984.15013MR1800003
  10. [10] Y. TIAN, The maximal and minimal ranks of some expressions of generalized inverses of matrices, Southeast Asian Bull. Math. 25 (2002), pp. 745-755. Zbl1007.15005MR1934671
  11. [11] Y. TIAN, Upper and lower bounds for ranks of matrix expressions using generalized inverses, Linear Algebra Appl. 355 (2002), pp. 187-214. Zbl1016.15003MR1930145
  12. [12] Y. TIAN - S. Cheng, The maximal and minimal ranks of A – BXC with applications, New York J. Math. 9 (2003), pp. 345-362. Zbl1036.15004MR2028174
  13. [13] H.J. WOERDEMAN, Minimal rank completions for block matrices, Linear Algebra Appl. 121 (1989), pp. 105-122. Zbl0681.15002MR1011731

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