Matrices and Graphs in Geometry / Miroslav Fiedler.

By: Fiedler, Miroslav
Material type: TextTextSeries: Encyclopedia of mathematics and its applications: 139.Publisher: Cambridge, UK ; New York : Cambridge University Press, 2011, ©2011Description: 1 online resource (viii, 197 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9781461938279; 1461938279; 9780511973611; 0511973616; 9781107387355; 1107387353; 9781107390232; 1107390230; 1139886576; 9781139886574; 1107299179; 9781107299177; 1107398657; 9781107398658Subject(s): Geometry | Matrices | Graphic methods | MATHEMATICS -- Topology | MATHEMATICS -- Geometry -- General | Geometry | Graphic methods | MatricesGenre/Form: Electronic book. | Electronic books. | Electronic books. Additional physical formats: Print version:: Matrices and Graphs in Geometry.DDC classification: 516 LOC classification: QA447 | .F45 2011ebOther classification: MAT038000 Online resources: Click here to access online
Contents:
Matricial approach to Euclidean geometry -- Simplex geometry -- Qualitative properties of the angles in a simplex -- Special simplexes -- Further geometric objects -- Applications.
Summary: "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.Summary: "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.
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"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.

"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.

Includes bibliographical references (pages 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.

Print version record.

English.

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