Introduction to Linear and Matrix Algebra PDF Download
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Author: Nathaniel Johnston
Publisher: Springer Nature
ISBN: 3030528111
Category : Mathematics
Languages : en
Pages : 482
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Book Description
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.
Author: Nathaniel Johnston
Publisher: Springer Nature
ISBN: 3030528111
Category : Mathematics
Languages : en
Pages : 482
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Book Description
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.
Author: Gilbert Strang
Publisher: Wellesley-Cambridge Press
ISBN: 9781733146630
Category : Mathematics
Languages : en
Pages : 368
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Book Description
Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.
Author: Richard C. Penney
Publisher: John Wiley & Sons
ISBN: 1118909593
Category : Mathematics
Languages : en
Pages : 510
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Book Description
Praise for the Third Edition “This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications.” – Electric Review A comprehensive introduction, Linear Algebra: Ideas and Applications, Fourth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique. The book introduces each new concept in the context of an explicit numerical example, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fourth Edition also features: Two new and independent sections on the rapidly developing subject of wavelets A thoroughly updated section on electrical circuit theory Illuminating applications of linear algebra with self-study questions for additional study End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB® code Linear Algebra: Ideas and Applications, Fourth Edition is an excellent undergraduate-level textbook for one or two semester courses for students majoring in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.
Author: Sheldon Axler
Publisher: Springer Science & Business Media
ISBN: 9780387982595
Category : Mathematics
Languages : en
Pages : 276
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Book Description
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Author: Library of Congress. Copyright Office
Publisher: Copyright Office, Library of Congress
ISBN:
Category : Copyright
Languages : en
Pages : 1140
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Book Description
Author: John Hamal Hubbard
Publisher:
ISBN: 9780971576674
Category : Algebras, Linear
Languages : en
Pages : 284
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Book Description
Author:
Publisher:
ISBN:
Category : Canada
Languages : en
Pages : 732
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Book Description
Author: Elmo Moore
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 132
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Book Description
Author: Jim Hefferon
Publisher: Orthogonal Publishing L3c
ISBN: 9780989897563
Category : Algebras, Linear
Languages : en
Pages :
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Book Description
"This text covers a standard first course : Gauss's method, vector spaces, linear maps and matrices, determinants, and eigenvalues and eigenvectors. In addition, each chapter ends with some topics such as brief applications. What sets it apart is careful motivation, many examples, and extensive exercise sets. Together these help each student master the material of this course, and also help an instructor develop that student's level of mathematical maturity. This book has been available online for many years and is widely used, both in classrooms and for self-study. It is supported by worked answers for all exercises, beamer slides for classroom use, and a lab manual of computer work"--Page 4 of cover.
Author: John Hamal Hubbard
Publisher:
ISBN: 9781943863013
Category :
Languages : en
Pages : 576
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Book Description
