Advanced Linear Algebra: With an Introduction to Module Theory (1版)

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【簡介】 Certain essential concepts in linear algebra cannot be fully explained in a first course. This is due to a lack of algebraic background for most beginning students. On the other hand, these concepts are taken for granted in most of the mathematical courses at graduate school level. This book will provide a gentle guidance for motivated students to fill the gap. It is not easy to find other books fulfilling this purpose. This book is a suitable textbook for a higher undergraduate course, as well as for a graduate student's self-study. The introduction of set theory and modules would be of particular interest to students who aspire to becoming algebraists. There are three parts to this book. One is to complete the discussion of bases and dimension in linear algebra. In a first course, only the finite dimensional vector spaces are treated, and in most textbooks, it will assume the scalar field is the real number field. In this book, the general case of arbitrary dimension and arbitrary scalar fields is examined. To do so, an introduction to cardinality and Zorn's lemma in set theory is presented in detail. The second part is to complete the proof of canonical forms for linear endomorphisms and matrices. For this, a generalization of vector spaces, and the most fundamental results regarding modules are introduced to readers. This will provide the natural entrance into a full understanding of matrices. Finally, tensor products of vector spaces and modules are briefly discussed. 【目錄】 1.Modules and Vector Spaces 2.Linear Maps 3.Determinant 4.Canonical Forms 5.A Brief Introduction to the Tensor Product

Introduction to Linear Algebra (6版)

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目錄 1. Introduction to vectors 2. Solving linear equations 3. Vector spaces and subspaces 4. Orthogonality 5. Determinants 6. Eigenvalues and eigenvectors 7. Linear transformations 8. Applications 9. Numerical linear algebra 10. Complex vectors and matrices

Introduction to Linear Algebra 6/e (6版)

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Introduction to Linear Algebra 6/e 作者：Gilbert Strang ISBN：9786269708109 年份：2023 出版商：New Moon Education 頁數/規格：440頁/平裝單色 Description Linear algebra now rivals or surpasses calculus in importance for people working in quantitative fields of all kinds: engineers, scientists, economists and business people. Gilbert Strang has taught linear algebra at MIT for more than 50 years and the course he developed has become a model for teaching around the world. His video lectures on MIT OpenCourseWare have been viewed over ten million times and his twelve textbooks are popular with readers worldwide. This sixth edition of Professor Strang's most popular book, Introduction to Linear Algebra, introduces the ideas of independent columns and the rank and column space of a matrix early on for a more active start. Then the book moves directly to the classical topics of linear equations, fundamental subspaces, least squares, eigenvalues and singular values – in each case expressing the key idea as a matrix factorization. The final chapters of this edition treat optimization and learning from data: the most active application of linear algebra today. Everything is explained thoroughly in Professor Strang's characteristic clear style. It is sure to delight and inspire the delight and inspire the next generation of learners. Table of Contents 1 Vectors and Matrices 2 Solving Linear Equations Ax = b 3 The Four Fundamental Subspaces 4 Orthogonality 5 Determinants 6 Eigenvalues and Eigenvectors 7 The Singular Value Decomposition (SVD) 8 Linear Transformations 9 Linear Algebra in Optimization 10 Learning from Data