참고문헌
- L. B. Beasley, Linear transformations which preserve fixed rank, Linear Algebra Appl. 40 (1981), 183-187. https://doi.org/10.1016/0024-3795(81)90148-8
- L. B. Beasley, Rank-k-preservers and preservers of sets of ranks, Linear Algebra Appl. 55 (1983), 11-17. https://doi.org/10.1016/0024-3795(83)90163-5
- L. B. Beasley and T. J. Laffey, Linear operators on matrices: the invariance of rank-k matrices, Linear Algebra Appl. 133 (1990), 175-184. https://doi.org/10.1016/0024-3795(90)90248-B
- L. B. Beasley, Erratum: "Linear operators on matrices: the invariance of rank-k matrices" [Linear Algebra Appl. 133 (1990), 175-184], Linear Algebra Appl. 180 (1993), 2.
- J. Bell and A. R. Sourour, Additive rank-one preserving mappings on triangular matrix algebras, Linear Algebra Appl. 312 (2000), no. 1-3, 13-33. https://doi.org/10.1016/S0024-3795(00)00024-0
- P. Botta, Linear maps preserving rank less than or equal to one, Linear and Multilinear Algebra 20 (1987), no. 3, 197-201. https://doi.org/10.1080/03081088708817756
- C. G. Cao, Modular automorphisms of upper triangular matrices over a commutative ring preserving rank one, Northeast. Math. J. 10 (1994), no. 4, 496-502.
- C. G. Cao and X. Zhang, Additive surjections preserving rank one and applications, Georgian Math. J. 11 (2004), no. 2, 209-217.
- W. L. Chooi and M. H. Lim, Linear preservers on triangular matrices, Linear Algebra Appl. 269 (1998), 241-255. https://doi.org/10.1016/S0024-3795(97)00069-4
- D. Z. Djokovic, Linear transformations of tensor products preserving a fixed rank, Pacic J. Math. 30 (1969), 411-414. https://doi.org/10.2140/pjm.1969.30.411
- B. Kuzma, Additive mappings preserving rank-one idempotents, ActaMath. Sin. (Engl. Ser.) 21 (2005), no. 6, 1399-1406. https://doi.org/10.1007/s10114-005-0598-1
- M. Marcus and B. N. Moyls, Linear transformations on algebras of matrices, Canad. J. Math. 11 (1959), 61-66. https://doi.org/10.4153/CJM-1959-008-0
- M. Marcus, Transformations on tensor product spaces, Pacic J. Math. 9 (1959), 1215-1221. https://doi.org/10.2140/pjm.1959.9.1215
- H. Minc, Linear transformations on matrices: rank 1 preservers and determinant preservers, Linear and Multilinear Algebra 4 (1976/77), no. 4, 265-272.
- L. Molnar and P. Semrl, Some linear preserver problems on upper triangular matrices, Linear and Multilinear Algebra 45 (1998), no. 2-3, 189-206. https://doi.org/10.1080/03081089808818586
- M. Omladic and P. Semrl, Additive mappings preserving operators of rank one, Linear Algebra Appl. 182 (1993), 239-256. https://doi.org/10.1016/0024-3795(93)90502-F
- R. S lowik, Maps on innite triangular matrices preserving idempotents, Linear and Multilinear Algebra 62 (2014), no. 7, 938-964. https://doi.org/10.1080/03081087.2013.801965
- W. C. Waterhouse, On linear transformations preserving rank one matrices over commutative rings, Linear and Multilinear Algebra 17 (1985), no. 2, 101-106. https://doi.org/10.1080/03081088508817646
피인용 문헌
- Bilocal automorphisms of T ∞(F) vol.48, pp.3, 2017, https://doi.org/10.1007/s13226-017-0235-6