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Alfred North Whitehead (1861-1947) was equally celebrated as a mathematician, a philosopher and a physicist. He collaborated with his former student Bertrand Russell on the first edition of Principia Mathematica (published in three volumes between 1910 and 1913), and after several years teaching and writing on physics and the philosophy of science at University College London and Imperial College, was invited to Harvard to teach philosophy and the theory of education. A Treatise on Universal Algebra was published in 1898, and was intended to be the first of two volumes, though the second (which was to cover quaternions, matrices and the general theory of linear algebras) was never published. This book discusses the general principles of the subject and covers the topics of the algebra of symbolic logic and of Grassmann's calculus of extension.

Algebra, Universal.

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Categories (Mathematics) --- 512.58 --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- 512.58 Categories. Category theory --- Categories. Category theory

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When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms. Covers hundreds of important and useful results on matrix theory, many never before available in any book Provides a list of symbols and a summary of conventions for easy use Includes an extensive collection of scalar identities and inequalities Features a detailed bibliography and author index with page references Includes an exhaustive subject index with cross-referencing

Matrices. --- Linear systems. --- Systems, Linear --- Differential equations, Linear --- System theory --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal

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This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.

Graph theory. --- Matrices. --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems

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Book description: Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to linear algebra, fourth edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, Fourier methods and the FFT, linear programming, and computer graphics. Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject

Algebras, Linear --- Algebra --- Mathematics --- Álgebra linear --- Algebras, Linear. --- 512.5 --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- 512.64 --- 512.64 Linear and multilinear algebra. Matrix theory --- Linear and multilinear algebra. Matrix theory --- Algebras, Linear - Textbooks. (LCSH - plus d'une traduction) --- Algebra - Textbooks. (LCSH - plus d'une traduction) --- Mathematics - Textbooks. (LCSH - plus d'une traduction)