Matrices and Graphs in Geometry [Hardcover]

Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.Comprising over 50 years of research, this book acquaints the reader with basic matrix theory, graph theory and elementary Euclidean geometry. Many readers will welcome this book, from undergraduates to specialists in mathematics, as well as non-specialists who only use mathematics occasionally.Comprising over 50 years of research, this book acquaints the reader with basic matrix theory, graph theory and elementary Euclidean geometry. Many readers will welcome this book, from undergraduates to specialists in mathematics, as well as non-specialists who only use mathematics occasionally.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.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.