The present monograph is a state-of-art survey of the geometry of matrices whose study was initiated by L K Hua in the forties. The geometry of rectangular matrices, of alternate matrices, of symmetric matrices, and of hermitian matrices over a division ring or a field are studied in detail. The author's recent results on geometry of symmetric matrices and of hermitian matrices are included. A chapter on linear algebra over a division ring and one on affine and projective geometry over a division ring are also included. The book is clearly written so that graduate students and third or fourth year undergraduate students in mathematics can read it without difficulty.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Fadenheftung
Pappband
mit Schutzumschlag
Maße
Höhe: 217 mm
Breite: 161 mm
Dicke: 27 mm
Gewicht
ISBN-13
978-981-02-2638-1 (9789810226381)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Chinese Academy Of Sciences, China
Part 1 Linear algebra over division rings: matrices over division rings; matrix representations of subspaces; systems of linear equations. Part 2 Affine geometry and projective geometry: affine spaces and affine groups; projective spaces and projective groups; one-dimensional projective geometry. Part 3 Geometry of rectangular matrices: the space of rectangular matrices; proof of the fundamental theorem; application to graph theory. Part 4 Geometry of alternate matrices: the space of alternate matrices; maximal sets. Part 5 Geometry of symmetric matrices: the space of symmetric matrices; proof of the fundamental theorem I-III. Part 6 Geometry of hermitian matrices: maximal sets of rank 1; proof of the fundamental theorem (the case n is greater than or equal to 3); the maximal set of rank 2 (n=2); proof of the fundamental theorem (the case n=2); and others.
