000			03105nmm a2200265Ia 4500
020			_a9780521461931
020			_a0521461936
082			_a516 _bF452M
100			_aFiedler, Miroslav. _917739
245		0	_aMatrices and Graphs in Geometry _c by Miroslav Fiedler.
260			_aCambridge, UK _aNew York _bCambridge University Press _c2011
300			_aviii, 197p. _bill.,25 cm.
490			_aEncyclopedia of Mathematics and its Applications
504			_aIncludes bibliographical references (p. [193]-194) and index.
505			_aMatricial approach to Euclidean geometry -- Simplex geometry -- Qualitative properties of the angles in a simplex --Special simplexes -- Further geometric objects -- Applications.
520			_a"Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and geometry can help in visualizing the behaviour of the problem. In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful. The author has discovered a method that in many (symmetric) cases helps to split huge systems into smaller parts. Many readers will welcome this book, from undergraduates to specialists in mathematics, as well as non-specialists who only use mathematics occasionally, and anyone who enjoys geometric theorems. It acquaints the reader with basic matrix theory, graph theory and elementary Euclidean geometry so that they too can appreciate the underlying connections between these various areas of mathematics and computer science"--Provided by publisher.
520			_a"This book comprises, in addition to auxiliary material, the research on which I have worked for the past more than 50 years. Some of the results appear here for the first time. The impetus for writing the book came from the late Victor Klee, after my talk in Minneapolis in 1991. The main subject is simplex geometry, a topic which fascinated me from my student times, caused, in fact, by the richness of triangle and tetrahedron geometry on one side and matrix theory on the other side. A large part of the content is concerned with qualitative properties of a simplex. This can be understood as studying not just relations of equalities but also inequalities. It seems that this direction is starting to have important consequences in practical (and important) applications, such as finite element methods"--Provided by publisher.
650			_aGeometry _917740
650			_aGraphs _917741
650			_aMathematics _917742
650			_aMatrices _aGraphic methods. _917743
830			_tEncyclopedia of mathematics and its applications _917744
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942			_cBK
999			_c13117 _d13117