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Advanced Linear and Matrix Algebra
Buch von Nathaniel Johnston
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor

Nathaniel Johnston is an Associate Professor of Mathematics at Mount Allison University in New Brunswick, Canada. His research makes use of linear algebra, matrix analysis, and convex optimization to tackle questions related to the theory of quantum entanglement. His companion volume, Introduction to Linear and Matrix Algebra, is also published by Springer.

Zusammenfassung

Motivates a deeper understanding of the abstract structures needed to tackle questions in mathematics, data analysis, and quantum information theory

Engages readers with a visual approach that uses color to enhance both content and learning

Features a wide selection of theoretical and applied topics to complement the core material

Incorporates exercises of all levels

Includes supplementary material: [...]

Inhaltsverzeichnis
Chapter 1: Vector Spaces.- Chapter 2: Matrix Decompositions.- Chapter 3: Tensors and Multilinearity.- Appendix A: Mathematical Preliminaries.- Appendix B: Additional Proofs.- Appendix C: Selected Exercise Solutions.
Details
Erscheinungsjahr: 2021
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xvi
494 S.
15 s/w Illustr.
108 farbige Illustr.
494 p. 123 illus.
108 illus. in color.
ISBN-13: 9783030528140
ISBN-10: 3030528146
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Johnston, Nathaniel
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Maße: 260 x 183 x 32 mm
Von/Mit: Nathaniel Johnston
Erscheinungsdatum: 20.05.2021
Gewicht: 1,266 kg
Artikel-ID: 118499041
Über den Autor

Nathaniel Johnston is an Associate Professor of Mathematics at Mount Allison University in New Brunswick, Canada. His research makes use of linear algebra, matrix analysis, and convex optimization to tackle questions related to the theory of quantum entanglement. His companion volume, Introduction to Linear and Matrix Algebra, is also published by Springer.

Zusammenfassung

Motivates a deeper understanding of the abstract structures needed to tackle questions in mathematics, data analysis, and quantum information theory

Engages readers with a visual approach that uses color to enhance both content and learning

Features a wide selection of theoretical and applied topics to complement the core material

Incorporates exercises of all levels

Includes supplementary material: [...]

Inhaltsverzeichnis
Chapter 1: Vector Spaces.- Chapter 2: Matrix Decompositions.- Chapter 3: Tensors and Multilinearity.- Appendix A: Mathematical Preliminaries.- Appendix B: Additional Proofs.- Appendix C: Selected Exercise Solutions.
Details
Erscheinungsjahr: 2021
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xvi
494 S.
15 s/w Illustr.
108 farbige Illustr.
494 p. 123 illus.
108 illus. in color.
ISBN-13: 9783030528140
ISBN-10: 3030528146
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Johnston, Nathaniel
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Maße: 260 x 183 x 32 mm
Von/Mit: Nathaniel Johnston
Erscheinungsdatum: 20.05.2021
Gewicht: 1,266 kg
Artikel-ID: 118499041
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