Keywords
skewsymmetric matrices
Hermitian matrices
linear preserver problems
How to Cite
Abstract
The central theorem in this paper characterizes linear transformations preserving both symmetric and skew-symmetric complex matrices. We also give some characterizations for complex orthogonal and unitary transformations preserving symmetric or Hermitian matrices.
References
Chi-Kwong Li & S. Pierce, Linear preserver problems. Amer. Mathe. Monthly, 108 (2001), .
Chi-Kwong Li & Nam-Kiu Tsing, Linear· Preserver Problems: A Brief lntroduction and Some Special Techniques.
M. Marcus & B . Moyls, Linear tranformations on algebras of matrices. Canad. J. Math. 11 (1959), 383-396.
D. Hill, Linear transformation which. preserve Hermitian matrices. Linear Algebra Áppl. 6 (1973), 257- 262.
C. Kunicki & D. Hill, Norm.al preserving linear transformations. Linear Algebra Appl. 170 (1992), 107- 115.
R.A. Horn & C .R. Jonhson, Matrix Analysis, Cambridge University Press, Cambridge, 1990.
R . Gro ne , Ch. Johnson, M. Sa & H. Wolkowicz , Normal matrices. Linear Algebra Appl. 87 (1987), 213-/225.
R.A. Horn & C. R. Jonhson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
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