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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.

Geometry --- Matrices --- Graphic methods --- Geometry. --- Matrices. --- Graphic methods. --- Graphics --- Graphs --- Geometrical drawing --- Least squares --- Mathematics --- Mechanical drawing --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Euclid's Elements

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Sparse matrices

Numerical analysis --- Sparse matrices. --- Matrices éparses. --- Analyse numérique. --- Algèbre linéaire. --- Algebras, Linear --- Matrices --- Algebra, Universal. --- Data processing. --- Data processing --- 519.6 --- 681.3*G13 --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Algebra, Multiple --- Multiple algebra --- N-way algebra --- Universal algebra --- Algebra, Abstract --- Numbers, Complex --- Analyse numérique --- Algèbre linéaire --- Numerical analysis. --- Algebras, Linear. --- Matrices - Data processing --- Calcul matriciel --- Methodes numeriques

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Whilst it is a moot point amongst researchers, linear algebra is an important component in the study of graphs. This book illustrates the elegance and power of matrix techniques in the study of graphs by means of several results, both classical and recent. The emphasis on matrix techniques is greater than other standard references on algebraic graph theory, and the important matrices associated with graphs such as incidence, adjacency and Laplacian matrices are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration, and the inclusion of exercises enables practical learning throughout the book. It may also be applied to a selection of sub-disciplines within science and engineering. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory who want to be acquainted with matrix theoretic ideas used in graph theory, it will also benefit a wider, cross-disciplinary readership.

Mathematics. --- Linear and Multilinear Algebras, Matrix Theory. --- Matrix theory. --- Mathématiques --- Graph theory --- Matrices --- Graph theory. --- Matrices. --- Graphentheorie. --- Electronic books. -- local. --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Graphs, Theory of --- Theory of graphs --- Extremal problems --- Algebra. --- Mathematical analysis --- Math --- Science --- Algebra, Abstract --- Algebra, Universal --- Combinatorial analysis --- Topology

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Mathematical statistics --- Multivariate analysis. --- Analyse multivariée --- Multivariate analysis --- 519.2 --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Matrices --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- Analyse multivariée

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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Control theory. --- Mathematical optimization. --- Matrices. --- Théorie de la commande --- Optimisation mathématique --- Matrices --- Control theory --- Mathematical optimization --- Théorie de la commande --- Optimisation mathématique --- EPUB-LIV-FT ELSEVIER-B --- Programming (Mathematics) --- Programmation (mathématiques) --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Dynamics --- Machine theory --- Programmation (mathématiques) --- Theorie du controle --- Theorie des systemes --- Programmation mathematique --- Systemes lineaires --- Controle stochastique --- Programmation lineaire