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Matrices and Graphs in Geometry /

Fiedler, Miroslav, (1926-)

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Matrices and Graphs in Geometry /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Matrices and Graphs in Geometry // Miroslav Fiedler.
作者:	Fiedler, Miroslav,
出版者:	Cambridge, UK ;Cambridge University Press, : 2011, ò011.,
面頁冊數:	viii, 197 p. :illustrations ;25 cm.
內容註:	Matricial approach to Euclidean geometry -- Simplex geometry -- Qualitative properties of the angles in a simplex --Special simplexes -- Further geometric objects -- Applications.
標題:	Geometry. -
電子資源:	http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-b.htmlContributor biographical information
電子資源:	http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-d.htmlPublisher description
電子資源:	http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-t.htmlTable of contents only
ISBN:	9780521461931(hbk.) :

Matrices and Graphs in Geometry /
Fiedler, Miroslav,1926-

Matrices and Graphs in Geometry /Miroslav Fiedler. - Cambridge, UK ;Cambridge University Press,2011, ò011. - viii, 197 p. :illustrations ;25 cm. - Encyclopedia of Mathematics and its Applications ;139.. - Encyclopedia of mathematics and its applications ;v. 124-125..

Includes bibliographical references (p. [193]-194) and index.

Matricial approach to Euclidean geometry -- Simplex geometry -- Qualitative properties of the angles in a simplex --Special simplexes -- Further geometric objects -- Applications.

"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.

ISBN: 9780521461931(hbk.) :US90.00Subjects--Topical Terms:

517251
Geometry.

LC Class. No.: QA447 / F45

Dewey Class. No.: 516

Matrices and Graphs in Geometry /
LDR:03165cam 2200289 i 4500 001 999443
003 OCoLC
005 20110425023212.0
008 120301t20112011enka b 001 0 eng
020 $a 9780521461931(hbk.) : $c US90.00
020 $a 0521461936
035 $a (OCoLC)689548773 $z (OCoLC)656771656
035 $a AS-BW-100-N-04
040 $a DLC $e rda $c DLC $d YDX $d CDX $d YDXCP $d UKM $d KMM $d YHM $d IXA
042 $a nbic
050 # 4 $a QA447 $b F45 $y 2011
082 0 0 $a 516 $2 22
100 1 $a Fiedler, Miroslav, $d 1926- $3 1325467
245 1 0 $a Matrices and Graphs in Geometry / $c Miroslav Fiedler.
260 # $a Cambridge, UK ; $a New York : $b Cambridge University Press, $c 2011, ò011.
300 $a viii, 197 p. : $b illustrations ; $c 25 cm.
490 1 0 $a Encyclopedia of Mathematics and its Applications ; $v 139.
504 $a Includes bibliographical references (p. [193]-194) and index.
505 0 # $a Matricial 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 # 0 $a Geometry. $3 517251
650 # 0 $a Matrices. $3 516894
650 # 0 $a Graphic methods. $3 636683
830 0 $a Encyclopedia of mathematics and its applications ; $v v. 124-125. $3 1232929
856 4 2 $z Contributor biographical information $u http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-b.html
856 4 2 $z Publisher description $u http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-d.html
856 4 1 $z Table of contents only $u http://catdir.loc.gov/catdir/enhancements/fy1101/2010046601-t.html