On Hua's fundamental theorem of the geometry of rectangular matrices

DOI10.1006/jabr.2001.9052zbMath1003.15013OpenAlexW2035810787MaRDI QIDQ1604394

Peter Šemrl

Publication date: 4 July 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2001.9052

zbMATH Keywords

adjacency preserving mappinggeometry of rectangular matricesmild hypothesis characterizationreal rectangular matrix

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Distance in graphs (05C12) Algebraization in linear incidence geometry (51A25)

Related Items (18)

Maps on matrix spaces ⋮ Adjacency preserving maps on upper triangular matrix algebras ⋮ The optimal version of Hua's fundamental theorem of geometry of square matrices -- the low dimensional case ⋮ Linear/additive preservers of ranks 2 and 4 on alternate matrix spaces over fields ⋮ Additive rank-one preservers between spaces of rectangular matrices ⋮ Adjacency preserving maps between exterior powers of vector spaces ⋮ Hua's fundamental theorem of the geometry of matrices. ⋮ Adjacency preserving maps on the space of symmetric operators ⋮ Nonlinear maps preserving solvability ⋮ Maps on idempotent matrices over division rings ⋮ Geometry of rectangular block triangular matrices ⋮ Geometry of block triangular matrices over a division ring ⋮ Hua's fundamental theorem of geometry of rectangular matrices over EAS division rings ⋮ A short proof of Hua's fundamental theorem of the geometry of Hermitian matrices. ⋮ Unnamed Item ⋮ Diameter preserving surjection on alternate matrices ⋮ Nonlinear preservers of group invertible operators ⋮ Hua's fundamental theorems of the geometry of matrices and related results

Cites Work

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• Non-Linear Spectrum-Preserving Maps
• Adjacency preserving maps on matrices and operators
• Geometries of Matrices. II. Study of Involutions in the Geometry of Symmetric Matrices
• Geometries of Matrices. III. Fundamental Theorems in the Geometries of Symmetric Matrices
• Automorphisms of the Field of Complex Numbers
• Geometries of Matrices. I 1 Arithmetical Construction
• Collinearity-preserving functions between Desarguesian planes

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