Overview

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.Contents: Linear Algebra over Division Rings: Matrices over Divison RingsMatrix Representations of SubspacesSystems of Linear Equations Affine Geometry and Projective Geometry: Affine Spaces and Affine GroupsProjective Spaces and Projective GroupsOne-Dimensional Projective Geometry Geometry of Rectangular Matrices: The Space of Rectangular MatricesProof of the Fundamental TheoremApplication to AlgebraApplication to GeometryApplication to Graph Theory Geometry of Alternate Matrices: The Space of Alternate MatricesMaximal Sets Geometry of Symmetric Matrices: The Space of Symmetric MatricesProof of the Fundamental Theorem I III Geometry of Hermitian Matrices: Maximal Sets of Rank 1Proof of the Fundamental Theorem (the Case n 3)Maximal Sets of Rank 2 (the Case n = 2)Proof of the Fundamental Theorem (the Case n = 2)and othersReadership: Graduate students in mathematics and mathematicians.

Full Product Details

9781299662285

Table of Contents

Reviews

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available