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This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is mainly theoretical in character, introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part, where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part includes factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structures. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike.

Algebra --- Numerical analysis --- Mathematics --- algebra --- matrices --- wiskunde --- numerieke analyse --- Matrix theory. --- Algebra. --- Numerical analysis. --- Linear and Multilinear Algebras, Matrix Theory. --- Numerical Analysis.

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This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

Algebra --- algebra --- lineaire algebra --- Algebra. --- Algebras, Linear. --- Matrix theory. --- Àlgebra lineal --- Matrius (Matemàtica)

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General biophysics --- General biochemistry --- Collagen --- Connective tissues --- Collagène --- Tissu conjonctif --- Periodicals --- Périodiques --- Collagen. --- Connective Tissue. --- Extracellular Matrix. --- Connective tissues. --- Périodiques. --- Connective Tissues --- Tissue, Connective --- Tissues, Connective --- Matrix, Extracellular --- Extracellular Matrices --- Matrices, Extracellular --- Avicon --- Avitene --- Collagen Felt --- Collagen Fleece --- Collagenfleece --- Collastat --- Dermodress --- Microfibril Collagen Hemostat --- Pangen --- Zyderm --- alpha-Collagen --- Collagen Hemostat, Microfibril --- alpha Collagen --- Connective Tissue --- Rheumatology --- Life Sciences --- Cytology, Cell Biology --- Micro and Molecular Biology --- Health Sciences --- Physiology --- Rheumatology. --- Life Sciences. --- Micro and Molecular Biology. --- biochemie --- Extracellular Matrix --- Connective tissue

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The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, the Lebesgue integral, vector calculus and differential equations. After having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today.

Algebra --- Algebraic geometry --- Functional analysis --- Differential equations --- Mathematical analysis --- Mathematics --- Mathematical physics --- differentiaalvergelijkingen --- algebra --- analyse (wiskunde) --- complexe veranderlijken --- reeksen (wiskunde) --- matrices --- functies (wiskunde) --- wiskunde --- Functions of real variables. --- Matrix theory. --- Algebra. --- Measure theory. --- Functions of complex variables. --- Differential equations. --- Sequences (Mathematics) --- Real Functions. --- Linear and Multilinear Algebras, Matrix Theory. --- Measure and Integration. --- Functions of a Complex Variable. --- Ordinary Differential Equations. --- Sequences, Series, Summability.

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Algebras, Linear --- Topological algebras --- Algebras, Linear. --- Topological algebras. --- functional analysis --- operator theory --- convex analysis --- matrix analysis --- control and optimization --- combinatorial linear algebra --- Algebras, Topological --- Functional analysis --- Linear topological spaces --- Rings (Algebra) --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Mathematics