Linear Algebra and GeometryCRC Press, 1 de out. de 1997 - 320 páginas This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metic, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics. |
Conteúdo
Linear Mappings | 3 |
Euclidean Spaces | 117 |
Orthogonal and Unitary Operators | 134 |
SelfAdjoint Operators in Quantum Mechanics | 148 |
ThreeDimensional Euclidean Space | 164 |
Minkowski Space | 173 |
Symplectic Space | 184 |
Witts Theorem and Witts Group | 187 |
Projective Groups and Projections | 233 |
Desargues and Pappus Configurations and Classical Projective Geometry | 242 |
The Kahler Metric | 247 |
Algebraic Varieties and Hilbert Polynomials | 249 |
Multilinear Algebra | 258 |
Canonical Isomorphisms and Linear Mappings of Tensor Products | 263 |
The Tensor Algebra of a Linear Space | 269 |
Classical Notation | 271 |
Clifford Algebras | 190 |
Affine and Projective Geometry | 195 |
Affine Groups | 203 |
Affine Subspaces | 207 |
Convex Polyhedra and Linear Programming | 215 |
Affine Quadratic Functions and Quadrics | 218 |
Projective Spaces | 222 |
Projective Duality and Projective Quadrics | 228 |
Symmetric Tensors | 276 |
SkewSymmetric Tensors and the Exterior Algebra of a Linear Space | 279 |
Exterior Forms | 290 |
Tensor Fields | 293 |
Tensor Products in Quantum Mechanics | 297 |
303 | |
Outras edições - Ver todos
Linear Algebra and Geometry P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin Visualização parcial - 1989 |