Matrices and Graphs in Geometry

0356557 - ÚI 2011 RIV GB eng B - Monografie kniha jako celek
Fiedler, Miroslav
Matrices and Graphs in Geometry.
Cambridge: Cambridge University Press, 2011. 206 s. Encyclopedia of Mathematics and Its Applications, 139. ISBN 978-0-521-46193-1
Výzkumný záměr: CEZ:AV0Z10300504
Klíčová slova: Euclidean space * graph * matrix * simplex * orthocentric simplex * cyclic simplex * hyperacute simplex * spherical simplex * inverse simplex * angle * face * triangle * tetrahedron * simplicial cone * polar cone * Menger matrix * Gramian * Laplacian matrix * resistive electrical network
Kód oboru RIV: BA - Obecná matematika
http://aleph.lib.cas.cz/F/?func=direct&doc_number=000875449&local_base=AV

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.
Trvalý link: http://hdl.handle.net/11104/0195050