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Periodical
SIAM journal on matrix analysis and applications.
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ISSN: 10957162 08954798 Publisher: [Philadelphia] : Society for Industrial and Applied Mathematics

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Abstract

A journal on linear algebra with emphasis on applications and numerical procedures.


Book
Advanced linear and matrix algebra
Author:
ISBN: 3030528154 3030528146 Year: 2021 Publisher: Cham, Switzerland : Springer,

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Abstract

This textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques. Beginning with a study of vector spaces that includes coordinates, isomorphisms, orthogonality, and projections, the book goes on to focus on matrix decompositions. Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. In each case, the author ties the new technique back to familiar ones, to create a coherent set of tools. Tensors and multilinearity complete the book, with a study of the Kronecker product, multilinear transformations, and tensor products. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section. Advanced Linear and Matrix Algebra offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. A first course in proof-based linear algebra is assumed. An ideal preparation can be found in the author’s companion volume, Introduction to Linear and Matrix Algebra.


Book
Introduction to matrix theory
Author:
ISBN: 303080481X 3030804801 Year: 2021 Publisher: Cham, Switzerland : Springer,

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Abstract

This book is designed to serve as a textbook for courses offered to undergraduate and postgraduate students enrolled in Mathematics. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schurtriangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition, and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least-squares solutions. The book includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics in the book are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts, and problems have been added at the end of each chapter. Most of these problems are theoretical, and they do not fit into the running text linearly. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in senior undergraduate and beginning postgraduate mathematics courses.

Keywords

Algebras, Linear. --- Engineering mathematics. --- Mathematical physics. --- Linear Algebra. --- Engineering Mathematics. --- Mathematical Physics. --- Physical mathematics --- Physics --- Engineering --- Engineering analysis --- Mathematical analysis --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology --- Mathematics --- Matrices. --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Matrius (Matemàtica) --- Àlgebra lineal --- Matemàtica per a enginyers --- Física matemàtica --- Mecànica --- Acústica --- Anàlisi de sistemes --- Anàlisi dimensional --- Grups quàntics --- Elasticitat --- Equació de Yang-Baxter --- Matemàtica en l'electrònica --- Problemes de contorn --- Teoria del potencial (Física) --- Teoria ergòdica --- Teories no lineals --- Rutes aleatòries (Matemàtica) --- Anàlisi matemàtica --- Mecànica aplicada --- Àlgebra universal --- Espais generalitzats --- Àlgebra tensorial --- Àlgebra vectorial --- Àlgebres de Clifford --- Àlgebres de Jordan --- Àlgebres de Lie --- Complexos (Matemàtica) --- Espais vectorials --- Topologia --- Àlgebra de matrius --- Àlgebra matricial --- Càlcul de matrius --- Càlcul matricial --- Matrius (Àlgebra) --- Àlgebra abstracta --- Anàlisi multivariable --- Desigualtats matricials --- Diagrames de Feynman --- Grups modulars --- Jocs d'estratègia (Matemàtica) --- Matrius aleatòries --- Matrius disperses --- Programació lineal

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