X WAN Z (EN) — GEOMETRY OF MATRICES

GEOMETRY OF MATRICES краткое содержание

GEOMETRY OF MATRICES - описание и краткое содержание, автор X WAN Z (EN), читать бесплатно онлайн на сайте электронной библиотеки Lib-King.Ru.

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 EquationsAffine Geometry and Projective Geometry:Affine Spaces and Affine GroupsProjective Spaces and Projective GroupsOne-Dimensional Projective GeometryGeometry of Rectangular Matrices:The Space of Rectangular MatricesProof of the Fundamental TheoremApplication to AlgebraApplication to GeometryApplication to Graph TheoryGeometry of Alternate Matrices:The Space of Alternate MatricesMaximal SetsGeometry of Symmetric Matrices:The Space of Symmetric MatricesProof of the Fundamental Theorem I – IIIGeometry 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.Key Features:Includes five new chaptersA complete and comprehensive description of Broad Relativity, which generalizes Einstein's original theory of special relativity to new physical time systems and a limited class of non-inertial framesBrings a fresh viewpoint with new physical implications and predictions to old physicsGives an updated discussion on fundamental physical constants and unit systems and their influence on the development of relativity theories