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Matrices and Graphs in Geometry

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: February 2011
  • availability: Available
  • format: Hardback
  • isbn: 9780521461931

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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.

    • Mathematical explanations are accessible to non-specialists
    • Helps the reader to understand and visualise geometry in higher dimensions
    • Contains applications to various fields, including electrical networks
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    Product details

    • Date Published: February 2011
    • format: Hardback
    • isbn: 9780521461931
    • length: 206 pages
    • dimensions: 240 x 165 x 16 mm
    • weight: 0.47kg
    • contains: 10 b/w illus.
    • availability: Available
  • Table of Contents

    1. A matricial approach to Euclidean geometry
    2. Qualitative properties of the angles in a simplex
    3. Special simplexes
    4. Further geometric objects
    5. Applications
    Appendix
    References
    Index.

  • Author

    Miroslav Fiedler, Academy of Sciences of the Czech Republic, Prague
    Miroslav Fiedler is Professor Emeritus in the Institutes of Mathematics and of Computer Science at the Academy of Sciences of the Czech Republic. His many awards include the Hans Schneider Prize from the International Linear Algebra Society (ILAS) and the Medal for Merits from the President of the Czech Republic.

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