The present monograph is a state-of-the-art survey of the geometry of matrices whose study was initiated by L.K. Hua in the 1940s. 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.

lgli/Geometry of Matrices.pdf

lgrsnf/Geometry of Matrices.pdf

zlib/Mathematics/Geometry and Topology/Che-Hsien Wan, Zhe-Xian Wan, Lo-Keng Hua/Geometry of Matrices: In Memory of Professor L K Hua_1298248.pdf

Zhe-Xian Wan; Zhexian Wan

World Scientific Publishing Co Pte Ltd

World Scientific Publishing Company

World Scientific Publishing Company, Singapore, 1996

Singapore, River Edge, N.J, Singapore, 1996

Singapore [etc, cop. 1996

0

lg874604

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"In memory of Professor L.K. Hua (1910-1985)."
Includes bibliographical references and index.

Includes bibliographical references (p. 367-370) and index.

1. Linear algebra over division rings. 1.1. Vector spaces over division rings. 1.2. Matrices over division rings. 1.3. Matrix representations of subspaces. 1.4. Systems of linear equations. 1.5. Hermitian, symmetric, and alternate matrices. 1.6. Comments -- 2. Affine geometry and projective geometry. 2.1. Affine spaces and affine groups. 2.2. Fundamental theorem of the affine geometry. 2.3. Projective spaces and projective groups. 2.4. Fundamental theorem of the projective geometry. 2.5. One-dimensional projective geometry. 2.6. Comments -- 3. Geometry of rectangular matrices. 3.1. The space of rectangular matrices. 3.2. Maximal sets of rank 1. 3.3. Maximal sets of rank 2. 3.4. Proof of the fundamental theorem. 3.5. Application to algebra. 3.6. Application to geometry. 3.7. Application to geometry (continued). 3.8. Application to graph theory. 3.9. Comments -- 4. Geometry of alternate matrices. 4.1. The space of alternate matrices. 4.2. Maximal sets. 4.3. Proof of the fundamental theorem. 4.4. Application to geometry. 4.5. Application to geometry (continued). 4.6. Application to graph theory. 4.7. Comments -- 5. Geometry of symmetric matrices. 5.1. The space of symmetric matrices. 5.2. Maximal sets of rank 1. 5.3. Maximal sets of rank 2 (characteristic not two). 5.4. Proof of the fundamental theorem (I). 5.5. Maximal sets of rank 2 (characteristic two). 5.6. Proof of the fundamental theorem (II). 5.7. Proof of the fundamental theorem (III). 5.8. Application to algebra. 5.9. Application to geometry. 5.10. Application to graph theory. 5.11. Comments -- 6. Geometry of hermitian matrices. 6.1. The space of hermitian matrices. 6.2. Maximal sets of rank 1. 6.3. Maximal sets of rank 2. 6.4. Proof of the fundamental theorem (the case n [symbol] 3). 6.5. Maximal sets of rank 2 (the case n = 2). 6.6. Proof of the fundamental theorem (the case n = 2). 6.7. Application to algebra. 6.8. Application to geometry. 6.9. Application to graph theory. 6.10. Comments

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.

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 graudate students and third or fourth year undergraduate students in mathematics can read it without difficulty.

This text is a survey of the geometry of matrices whose study was initiated by L.K. Hua in the 1940s.The geometry of rectangular matrices and of hermitian matrices over a division ring or a field are studied in detail.

State of the art survey of geometry of matrices. Professor L. K. Hua initiated work in this area in the middle forties

2012-12-30