References
- Bostian , AA and Woerdeman , HJ . 2001 . Unicity of minimal rank completions for tri-diagonal partial block matrices . Linear Algebra Appl. , 325 : 23 – 55 .
- Burns , F , Carlson , D , Haynsworth , E and Markham , T . 1974 . Generalized inverse formulae using the Schur complements . SIAM J. Appl. Math. , 26 : 254 – 259 .
- Carlson , D . 1986 . What are Schur complements, anyway? . Linear Algebra Appl. , 74 : 257 – 275 .
- Cohen , N , Johnson , CR , Rodman , L and Woerdeman , HJ . 1989 . Ranks of completions of partial matrices . Oper. Theory: Adv. Appl. , 40 : 165 – 185 .
- Davis , C . 1988 . Completing a matrix so as to minimize its rank . Oper. Theory: Adv. Appl. , 29 : 87 – 95 .
- De Moor , B and Golub , GH . 1991 . The restricted singular value decomposition: properties and applications . SIAM J. Matrix Anal. Appl. , 12 : 401 – 425 .
- Johnson , CR . 1990 . Matrix completion problems: a survey in matrix theory and applications . Proc. Sympos. Appl. Math. AMS , 40 : 171 – 197 .
- Johnson , CR and Whitney , GT . 1991 . Minimum rank completions . Linear Multilinear Algebra , 28 : 271 – 273 .
- Marsaglia , G and Styan , GPH . 1974 . Equalities and inequalities for ranks of matrices . Linear Multilinear Algebra , 2 : 269 – 292 .
- Penrose , R . 1955 . A generalized inverse for matrices . Proc. Cambridge Philos. Soc. , 51 : 406 – 413 .
- Tian , Y . 2000 . Completing block matrices with maximal and minimal ranks . Linear Algebra Appl. , 321 : 327 – 345 .
- Tian , Y . 2002 . The minimum rank of a 3 × 3 partial block matrix . Linear Multilinear Algebra , 50 : 125 – 131 .
- Tian , Y . 2002 . The maximal and minimal ranks of some expressions of generalized inverses of matrices . Southeast Asian Bull. Math. , 25 : 745 – 755 .
- Tian , Y . 2002 . Upper and lower bounds for ranks of matrix expressions using generalized inverses . Linear Algebra Appl. , 355 : 187 – 214 .
- Tian , Y . 2002 . The minimal ranks of the matrix expression A − BX − YC . Missouri J. Math. Sci. , 14 : 40 – 48 .
- Tian , Y and Cheng , S . 2003 . The maximal and minimal ranks of A − BXC with applications . New York J. Math. , 9 : 345 – 362 .
- Tian , Y and Liu , Y . 2006 . Extremal ranks of some symmetric matrix expressions with applications . SIAM J. Matrix Anal. Appl. , 28 : 890 – 905 .
- Woerdeman , HJ . 1987 . The lower order of triangular operators and minimal rank extensions . Integral Equ. Oper. Theory , 10 : 859 – 879 .
- Woerdeman , HJ . 1989 . Minimal rank completions for block matrices . Linear Algebra Appl. , 121 : 105 – 122 .
- Woerdeman , HJ . 1993 . Minimal rank completions of partial banded matrices . Linear Multilinear Algebra , 36 : 59 – 69 .