000			a
999			_c31070 _d31070
008			220823b xxu||||| |||| 00| 0 eng d
020			_a9780367372880
082			_a512.5 _bLOE
100			_aLoehr, Nicholas
245			_aAdvanced linear algebra
260			_bCRC Press, _c2014 _aBoca Raton :
300			_axxii, 609 p. ; _bill., _c25 cm
365			_b4995.00 _cINR _d01
490			_aTextbooks in mathematics
504			_aIncludes bibliographical references.
520			_aWhat is linear algebra, and how is it used? Upon examining almost any introductory text on linear algebra, we find a standard list of topics that seems to define the subject. On one hand, one part of linear algebra consists of computational techniques for solving linear equations, multiplying and inverting matrices, calculating and interpreting determinants, finding eigenvalues and eigenvectors, and so on. On the other hand, there is a theoretical side to linear algebra involving abstract vector spaces, subspaces, linear independence, spanning sets, bases, dimension, and linear transformations. But there is much more to linear algebra than just vector spaces, matrices, and linear equations! The goal of this book is to explore a variety of advanced topics in linear algebra, which highlight the rich interconnections linking this subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The book consists of twenty chapters, grouped into six main subject areas (algebraic structures, matrices, structured matrices, geometric aspects of linear algebra, modules, and multilinear algebra). Some chapters approach introductory material from a more sophisticated or abstract viewpoint; other chapters provide elementary expositions of more theoretical concepts; yet other chapters offer unusual perspectives or novel treatments of standard results. Unlike some advanced mathematical texts, this book has been carefully designed to minimize the dependence of each chapter on material found in earlier chapters. Each chapter has been conceived as a "mathematical vignette" devoted to the development of one specific topic.
650			_aBackground on algebraic structures
650			_aMatrices with special structure
650			_aAffine Combination
650			_a Banch Space
650			_a Cancellation law
650			_a Cayley -Hamilton theorem
650			_a Diagonalizable part, linear map
650			_a Euclidean plane
650			_aFree commutative group
650			_aFundamental homomorphism theorem
650			_a Generalized distributive law
650			_aHereditary system
650			_a Identity function
650			_a Jordan canoical form theorem
650			_aLinear map
650			_a Maximal chain
650			_aNested quotient isomorphism theorem
650			_aOne-to-one function
650			_a Parallelogram law
650			_a Quartic formula
650			_aRadon's theorem
650			_a Schroder-Bernstein theorem
650			_aTriangle inequality
650			_aUniversal mapping property
650			_aVector space
650			_aZorn's lemma
942			_2ddc _cBK