Geometry of matrices
著者
書誌事項
Geometry of matrices
World Scientific, c1996
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注記
"In memory of Professor L.K. Hua (1910-1985)"
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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