Idempotence-preserving maps between matrix spaces over fields of characteristic 2.
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Immanant Conversion on Symmetric Matrices
M. Purificação Coelho, M. Antónia Duffner, Alexander E. Guterman (2014)
Special Matrices
Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(Φ(Α ) + αΦ(Β)) for all matrices A,В ε Σ„(С) and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С).
Invertible commutativity preservers of matrices over max algebra
Seok-Zun Song, Kyung-Tae Kang, Young Bae Jun (2006)
Czechoslovak Mathematical Journal
The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We characterize the invertible linear operators that preserve the set of commuting pairs of matrices over a subalgebra of max algebra.
Involutions and semiinvolutions
Hiroyuki Ishibashi (2006)
Czechoslovak Mathematical Journal
We define a linear map called a semiinvolution as a generalization of an involution, and show that any nilpotent linear endomorphism is a product of an involution and a semiinvolution. We also give a new proof for Djocović’s theorem on a product of two involutions.
Isometries of E2.
Stephen Pierce, William Watkins (1979)
Journal für die reine und angewandte Mathematik
Iteration einer n-Ecksabbildung.
M. Adelmeyer, D. Stoffer (1996)
Elemente der Mathematik
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