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Matrices and Graphs in Geometry
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SYSNO ASEP 0356557 Druh ASEP B - Monografie Zařazení RIV B - Odborná monografie, kniha Název Matrices and Graphs in Geometry Tvůrce(i) Fiedler, Miroslav (UIVT-O) SAI, RID Vyd. údaje Cambridge: Cambridge University Press, 2011 ISBN 978-0-521-46193-1 Edice Encyclopedia of Mathematics and Its Applications Č. sv. edice 139 Poč.str. 206 s. Poč.výt. 1000 Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. 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 Vědní obor RIV BA - Obecná matematika CEZ AV0Z10300504 - UIVT-O (2005-2011) DOI 10.1017/CBO9780511973611 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2011
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