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Twelfth edition of a classical textbook on Linear Algebra.

Algebras, Linear. --- Algebra, Universal.

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This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics.The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variation

Operator theory. --- Matrices. --- Spectral theory (Mathematics) --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal

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Algebra, Abstract --- Algèbre abstraite --- 512.5 --- 512.5 General algebra --- General algebra --- Abstract algebra --- Algebra, Universal --- Logic, Symbolic and mathematical --- Set theory --- Algèbre --- Algebra --- Algèbre linéaire --- Algebras, Linear --- Groupes, Théorie des --- Group theory

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J-contractive and J-inner matrix valued functions have a wide range of applications in mathematical analysis, mathematical physics, control engineering and theory of systems and networks. This book provides a comprehensive introduction to the theory of these functions with respect to the open upper half-plane, and a number of applications are also discussed. The first chapters develop the requisite background material from the geometry of finite dimensional spaces with an indefinite inner product, and the theory of the Nevanlinna class of matrix valued functions with bounded characteristic in the open upper half-plane (with attention to special subclasses). Subsequent chapters develop this theory to include associated pairs of inner matrix valued functions and reproducing kernel Hilbert spaces. Special attention is paid to the subclasses of regular and strongly regular J-inner matrix valued functions, which play an essential role in the study of the extension and interpolation problems.

Functions of complex variables. --- Functions. --- Analysis (Mathematics) --- Differential equations --- Mathematical analysis --- Mathematics --- Numbers, Complex --- Set theory --- Calculus --- Complex variables --- Elliptic functions --- Functions of real variables --- Matrices. --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal

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Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field.

Algebra, Homological. --- Categories (Mathematics) --- Algebraic topology. --- Combinatorial topology. --- Topology --- Complexes --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Functor theory --- Homological algebra --- Algebra, Abstract --- Homology theory --- Combinatorics. --- Algebraic Topology. --- Combinatorics --- Algebra --- Mathematical analysis --- Algebraic topology --- Combinatorial topology