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Reinhold Baer
Linear Algebra and Projective Geometry
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710075Linear Algebra and Projective Geometryhttps://www.gandhi.com.mx/linear-algebra-and-projective-geometry-1/phttps://gandhi.vtexassets.com/arquivos/ids/917187/98b68466-ff07-4d1f-9c74-12b639658486.jpg?v=638336761994930000264311MXNDover PublicationsInStock/Ebooks/<p>Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussions starting point, within algebraic structures such as the endomorphism ring of the underlying manifold or the full linear group.Restricted to topics of an algebraic nature, the text shows how far purely algebraic methods may extend. It assumes only a familiarity with the basic concepts and terms of algebra. The methods of transfinite set theory frequently recur, and for readers unfamiliar with this theory, the concepts and principles appear in a special appendix.</p>...707556Linear Algebra and Projective Geometry264311https://www.gandhi.com.mx/linear-algebra-and-projective-geometry-1/phttps://gandhi.vtexassets.com/arquivos/ids/917187/98b68466-ff07-4d1f-9c74-12b639658486.jpg?v=638336761994930000InStockMXN99999DIEbook20129780486154664_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_<p>Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussions starting point, within algebraic structures such as the endomorphism ring of the underlying manifold or the full linear group.<br />Restricted to topics of an algebraic nature, the text shows how far purely algebraic methods may extend. It assumes only a familiarity with the basic concepts and terms of algebra. The methods of transfinite set theory frequently recur, and for readers unfamiliar with this theory, the concepts and principles appear in a special appendix.</p>9780486154664_Dover Publicationslibro_electonico_441ea1e7-25e2-34ce-9d0e-fcc795109c26_9780486154664;9780486154664_9780486154664Reinhold BaerInglésMéxico2012-05-14T00:00:00+00:00https://getbook.kobo.com/koboid-prod-public/ingrooves-epub-78084ff2-7f44-4452-97b1-15ee000eeed6.epubDover Publications