000			03032nam a22004815i 4500
001			978-3-642-30994-6
003			DE-He213
005			20140220082849.0
007			cr nn 008mamaa
008			120823s2013 gw | s |||| 0|eng d
020			_a9783642309946 _9978-3-642-30994-6
024	7		_a10.1007/978-3-642-30994-6 _2doi
050		4	_aQA184-205
072		7	_aPBF _2bicssc
072		7	_aMAT002050 _2bisacsh
082	0	4	_a512.5 _223
100	1		_aShafarevich, Igor R. _eauthor.
245	1	0	_aLinear Algebra and Geometry _h[electronic resource] / _cby Igor R. Shafarevich, Alexey O. Remizov.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2013.
300			_aXXI, 526 p. 70 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface -- Preliminaries -- 1. Linear Equations -- 2. Matrices and Determinants -- 3. Vector Spaces -- 4. Linear Transformations of a Vector Space to Itself -- 5. Jordan Normal Form -- 6. Quadratic and Bilinear Forms -- 7. Euclidean Spaces -- 8. Affine Spaces -- 9. Projective Spaces -- 10. The Exterior Product and Exterior Algebras -- 11. Quadrics -- 12. Hyperbolic Geometry -- 13. Groups, Rings, and Modules -- 14. Elements of Representation Theory -- Historical Note -- References -- Index.
520			_aThis book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aMatrix theory.
650		0	_aGeometry.
650	1	4	_aMathematics.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
650	2	4	_aAlgebra.
650	2	4	_aGeometry.
650	2	4	_aAssociative Rings and Algebras.
700	1		_aRemizov, Alexey O. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642309939
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-30994-6
912			_aZDB-2-SMA
999			_c97049 _d97049