45
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Linear preservers of orthogonal decomposable Tensors

Pages 333-354 | Received 19 Jul 1999, Published online: 31 Mar 2008

References

  • Chan , G. H. and Lim , M. H. 1992 . Linear transformations on symmetric matrices: II . Linear and Multilinear Algebra , 32 : 319 – 325 .
  • Chan , G. H. and Lim , M. H. 1995 . Linear preservers of decomposable tensors . Linear and Multilinear Algebra , 40 : 171 – 181 .
  • Cummings , L. 1970 . Decomposable symmetric tensors . Pacific J. Math. , 35 : 65 – 77 .
  • Cummings , L. 1972 . Transformations of symmetric tensors . Pacific J. Math. , 42 : 603 – 613 .
  • Dias da Silva , J. A. 1993 . A note on preservers of decomposability . Linear Algebra Appl. , 186 : 215 – 225 .
  • Dixon , J. D. 1977 . Rigid embeddings of simple groups in the general linear group . Canad. J. Math. , 29 : 384 – 391 .
  • Grone , R. 1977 . Decomposable tensors as a quadratic variety . Proc. Amer. Math. Soc , 64 : 227 – 230 .
  • Horn , R. A. , Li , C.-K. and Tsing , N.-K. 1991 . Linear operators preserving certain equivalence relations on matrices . Siam J. Matrix Anal. Appl. , 12 : 195 – 204 .
  • Li , C.-K. and Tsing , N.-K. 1993 . Linear operators leaving a class of matrices with fixed singular values invariant . Linear and Multilinear Algebra , 34 : 41 – 49 .
  • Lim , M. H. 1974 . Linear transformations on symmetric spaces . Pacific J. Math. , 55 : 499 – 505 .
  • Lim , M. H. 1975 . Linear transformations of tensor spaces preserving decomposable vectors . Publ. Inst. Math. , 18 ( 32 ) Beograd N.S
  • Lim , M. H. 1976 . Linear transformations on symmetry classes of tensors . Linear and Multilinear Algebra , 3 ( 32 ) : 267 – 280 .
  • Lim , M. H. 1979 . Linear transformations on symmetric matrices . Linear and Multilinear Algebra , 3 ( 32 ) : 47 – 57 .
  • Lim , M. H. 1990 . Linear mappings on second symmetric product spaces that preserve rank less than or equal to one . Linear and Multilinear Algebra , 26 ( 32 ) : 187 – 193 .
  • Lim , M. H. 1990 . Linear transformations on symmetry classes of tensors II . Linear and Multilinear Algebra , 26 ( 32 ) : 195 – 205 .
  • Lim , M. H. 1991 . Linear maps on symmetric spaces: The invariance of nonzero decomposable elements . Linear Algebra Appl. , 148 ( 32 ) : 89 – 92 .
  • Lim , M. H. 1992 . Conditions on decomposable symmetric tensors as an algebraic variety . Linear and Multilinear Algebra , 32 ( 32 ) : 249 – 252 .
  • Lim , M. H. 1993 . Linear transformations on symmetric spaces II . Canad. J. Math. , 45 ( 32 ) : 357 – 368 .
  • Lim , M. H. 1997 . Invertible preservers of certain decomposable tensors . Linear Algebra Appl. , 266 ( 32 ) : 153 – 159 .
  • Lim , M. H. 1997 . Linear preservers of decomposable symmetric tensors . Linear and Multilinear Algebra , 42 ( 32 ) : 291 – 302 .
  • Marcus , M. and Gordon , W. R. 1970 . The structure of bases in tensor spaces . Amer. J. Math. , 42 ( 32 ) : 623 – 640 .
  • Marcus , M. 1973 . Finite Dimensional Multilinear Algebra, Part I , New York : Marcel Dekker .
  • Marcus , M. 1975 . Finite Dimensional Multilinear Algebra, Part II , New York : Marcel Dekker .
  • Marcus , M. and Moyls , B. N. 1959 . Transformations on tensor product spaces . Pacific J. Math. , 9 : 1215 – 1221 .
  • Shaw , R. 1983 . Linear Algebra and Group Representations , Vol. 2 , New York : Academic Press .
  • Westwick , R. 1967 . Transformations on tensor spaces . Pacific J. Math. , 2 : 13 – 620 .
  • Westwick , R. 1995 . Transformations on tensor spaces II . Linear and Multilinear Algebra , 40 : 81 – 92 .
  • Westwick , R. 1996 . Decomposability under field extensions . Linear and Multilinear Algebra , 41 : 251 – 253 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.