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This monograph develops projective geometries and provides a systematic treatment of morphisms. It is unique in that it does not confine itself to isomorphisms. This work introduces a new fundamental theorem and its applications describing morphisms of projective geometries in homogeneous coordinates by semilinear maps. Other topics treated include three equivalent definitions of projective geometries and their correspondence with certain lattices; quotients of projective geometries and isomorphism theorems; recent results in dimension theory; morphisms and homomorphisms of projective geometries; special morphisms; duality theory; morphisms of affine geometries; polarities; orthogonalities; Hilbertian geometries and propositional systems. The book concludes with a large section of exercises. Audience: This volume will be of interest to mathematicians and researchers whose work involves projective geometries and their morphisms, semilinear maps and sesquilinear forms, lattices, category theory, and quantum mechanics. This book can also be recommended as a text in axiomatic geometry.
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Subjects
Projective Geometry, Mathematics, Science/Mathematics, General, Geometry - General, Geometry, Physics, Mathematics / Geometry / General, Medical-General, Geometry - Analytic, Geometry, Projective, Quantum theory, Combinatorial analysis, Algebra, Matrix theory, Matrix Theory Linear and Multilinear Algebras, Homological Algebra Category TheoryShowing 4 featured editions. View all 4 editions?
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Modern Projective Geometry (Mathematics And Its Applications Volume 521) (Mathematics and Its Applications)
August 1, 2000, Springer
Hardcover
in English
- 1 edition
0792365259 9780792365259
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