The Regular Shorted Matrix and the Hybrid Sum

Advances in Applied Mathematics - Tập 18 - Trang 403-422 - 1997
S.K. Mitra1, K. Manjunatha Prasad1
1Indian Statistical Institute Delhi Centre 7, SJS Sansanwal Marg New Delhi 110 016, India

Tài liệu tham khảo

Anderson, 1971, Shorted operator, SIAM J. Appl. Math., 20, 520, 10.1137/0120053 Anderson, 1969, Series and parallel addition of matrices, J. Math. Anal. Appl., 26, 576, 10.1016/0022-247X(69)90200-5 Anderson, 1975, Shorted operators, II, SIAM J. Appl. Math., 28, 60, 10.1137/0128007 Cramer, 1945 Duffin, 1972, Hybrid addition of matrices—A network theory concept, Appl. Anal., 2, 241, 10.1080/00036817208839042 Duffin, 1978, Almost definite operators ad electromechanical systems, SIAM J. Appl. Math., 35, 21, 10.1137/0135003 Hartwig, 1980, How to order regular elements, Math. Japon., 25, 1 Krein, 1947, The theory of self-adjoint extension of semibounded Hermitian transformations and its applications, I, II, Mat. Sb. N.S., 20, 431 Loeve, 1977 Mitra, 1982, Properties of the fundamental bordered matrix used in linear estimation Mitra, 1986, The minus partial order and shorted matrix, Linear Algebra Appl., 81, 207 Mitra, 1989, Block independence in generalized inverse: A coordinate free look, 429 Mitra, 1990, On DRD matrices, Gujarat Statist. Rev. (Prof. C. G. Khatri Memorial Volume), 40, 128 Mitra, 1994, Separation theorems, Linear Algebra Appl., 208/209, 238, 10.1016/0024-3795(94)90442-1 Mitra, 1996, The nonunique shorted matrix, Linear Algebra Appl., 237/238, 41, 10.1016/0024-3795(95)00599-4 Mitra, 1991, The shorted operator statistically interpreted, Calcutta Statist. Assoc. Bull. (Prof. H. K. Nandi Memorial Volume), 40, 157 S. K. Mitra, S. Puntanen, G. P. H. Styan, 1995, Shorted matrices and their applications in linear statistical models: A review, New Trends in Probability and Statistics, Proceedings, 5th Tartu Conference on Multivariate Statistics, Margit, Tiit, 289, 311, TEV Ltd. Vilnius, Lithuania Mitra, 1979, Shorted operators and generalized inverses of matrices, Linear Algebra Appl., 25, 45, 10.1016/0024-3795(79)90005-3 Mitra, 1982, Shorted matrix: An extended concept and some applications, Linear Algebra Appl., 42, 57, 10.1016/0024-3795(82)90138-0 Mitra, 1983, The fundamental bordered matrix of linear estimation and the Duffin–Morley general linear electromechanical systems, Appl. Anal., 14, 241, 10.1080/00036818308839428 Mitra, 1975, On hybrid addition of matrices, Linear Algebra Appl., 10, 19, 10.1016/0024-3795(75)90091-9 Rao, 1971, Unified theory of linear estimation, Sankhya Ser A, 33, 371 Rao, 1971