1 |
C. Davis, Completing a matrix so as to minimize its rank, Oper. Theory: Adv. Appl., 29 (1988), 87-95.
|
2 |
S.K. Mitra, Fixed rank solutions of linear matrix equations. Sankhya, Ser. A., 35 (1972), 387-392.
|
3 |
G. Marsaglia, G.P.H. Styan, Equalities and inequalities for ranks of matrices, Linear Multilinear Algebra, 2 (1974) 269-292.
DOI
|
4 |
Y. Tian, The Solvability of two linear matrix equations, Linear Multilinear Algebra 48 (2000), 123-147.
DOI
|
5 |
M.S. Wei, Q.W. Wang, On rank-constrained Hermitian nonnegtive-denite least squares solutions to the matrix equation AX A* = B, Int. J. Comput. Math., 84 (2007), 945-952.
DOI
ScienceOn
|
6 |
M. Mahajan, J. Sarma, On the complexity of matrix rank and rigidity, Lect. Notes Comput. Sci. Eng., 4649 (2007), 269-280.
DOI
ScienceOn
|
7 |
Q.F. Xiao, X.Y. Hu, L. Zhang, The symmetric minimal rank solution of the matrix equation AX = B and the optimal approximation, Electronic J. Linear Algebra, 18 (2009), 264-273.
|
8 |
Q. Zhang, Q.W. Wang, The (P,Q)-(skew)symmetric extremal rank solutions to a system of quaternion matrix equations, Appl. Math. Comput., 217 (2011) 9286-9296.
DOI
ScienceOn
|
9 |
Y. Tian, Y. Liu, Extremal ranks of some symmetric matrix expressions with applications, SIAM J. Matrix Anal. Appl., 28 (2006), 890-905.
DOI
ScienceOn
|
10 |
Y. Tian, Equalities and inequalities for inertias of Hermitian matrices with applications, Linear Algebra Appl., 433 (2010), 263-296.
DOI
ScienceOn
|
11 |
Y. Tian. Maximization and minimization of the rank and inertia of the Hermitian matrix expression A-BX-(BX)* with applications, Linear Algebra Appl., 434 (2011), 2109-2139.
DOI
ScienceOn
|
12 |
Y. Tian, On an equality and four inequalities for generalized inverses of Hermitian matrices, Electronic J. Linear Algebra, 23 (2012), 11-42.
|
13 |
F. Uhlig, On the matrix equation AX = B with applications to the generators of controllability matrix. Linear Algebra Appl., 85 (1987), 203-209.
DOI
ScienceOn
|
14 |
W.F. Trench, Hermitian, hermitian R-symmetric, and hermitian R-skew symmetric Procrustes problems, Linear Algebra Appl. 387 (2004), 83-98.
DOI
ScienceOn
|
15 |
M. Mesbahi, On the rank minimization problem and its control applications, Systems Control Lett., 33 (1998), 31-36.
DOI
ScienceOn
|
16 |
Y. Tian, Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method, Nonlinear Anal.: Theory, Meth. Appl., 75:2 (2012), 717-734.
DOI
ScienceOn
|
17 |
Y.H. Liu, Ranks of least squares solutions of the matrix equation AXB = C, Comput. Math. Appl., 55 (2008), 1270-1278.
DOI
ScienceOn
|
18 |
F.X. Zhang, Y. Li, W.B. Guo, J.L. Zhao, Least squares solutions with special structure to the linear matrix equation AXB = C, Appl. Math. Comput., 217:24 (2011), 10049-10057.
DOI
ScienceOn
|
19 |
F.X. Zhang, Y. Li, J.L. Zhao, Common Hermitian least squares solutions of matrix equations = and = and subject to inequality restrictions, Comput. Math. Appl. 62:6 (2011), 2424-2433.
DOI
ScienceOn
|
20 |
Ying Li, Yan Gao, Wenbin Guo, A Hermitian least squares solution of the matrix equation AXB = C subject to inequality restrictions, Comput. Math. Appl., 64:6 (2012), 1752-1760.
DOI
ScienceOn
|
21 |
Y. Tian, Rank equalities related to generalized inverses of matrices and their applications, Master Thesis, Montreal, Quebec, Canada, 2000. http://arxiv.org/abs/math/0003224vl.
|