The Less Is More Linear Algebra of Vector Spaces and Matrices
Title | The Less Is More Linear Algebra of Vector Spaces and Matrices PDF eBook |
Author | Daniela Calvetti |
Publisher | SIAM |
Pages | 181 |
Release | 2022-11-30 |
Genre | Mathematics |
ISBN | 1611977401 |
Designed for a proof-based course on linear algebra, this rigorous and concise textbook intentionally introduces vector spaces, inner products, and vector and matrix norms before Gaussian elimination and eigenvalues so students can quickly discover the singular value decomposition (SVD)—arguably the most enlightening and useful of all matrix factorizations. Gaussian elimination is then introduced after the SVD and the four fundamental subspaces and is presented in the context of vector spaces rather than as a computational recipe. This allows the authors to use linear independence, spanning sets and bases, and the four fundamental subspaces to explain and exploit Gaussian elimination and the LU factorization, as well as the solution of overdetermined linear systems in the least squares sense and eigenvalues and eigenvectors. This unique textbook also includes examples and problems focused on concepts rather than the mechanics of linear algebra. The problems at the end of each chapter that and in an associated website encourage readers to explore how to use the notions introduced in the chapter in a variety of ways. Additional problems, quizzes, and exams will be posted on an accompanying website and updated regularly. The Less Is More Linear Algebra of Vector Spaces and Matrices is for students and researchers interested in learning linear algebra who have the mathematical maturity to appreciate abstract concepts that generalize intuitive ideas. The early introduction of the SVD makes the book particularly useful for those interested in using linear algebra in applications such as scientific computing and data science. It is appropriate for a first proof-based course in linear algebra.
Vector Spaces and Matrices
Title | Vector Spaces and Matrices PDF eBook |
Author | Robert M. Thrall |
Publisher | Courier Corporation |
Pages | 340 |
Release | 2014-01-15 |
Genre | Mathematics |
ISBN | 0486321053 |
Students receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. Suitable as a primary or supplementary text for college-level courses in linear algebra. 1957 edition.
Linear Vector Spaces and Cartesian Tensors
Title | Linear Vector Spaces and Cartesian Tensors PDF eBook |
Author | James Kenyon Knowles |
Publisher | Oxford University Press on Demand |
Pages | 120 |
Release | 1998 |
Genre | Mathematics |
ISBN | 9780195112542 |
Linear Vector Spaces and Cartesian Tensors is primarily concerned with the theory of finite dimensional Euclidian spaces. It makes a careful distinction between real and complex spaces, with an emphasis on real spaces, and focuses on those elements of the theory that are especially important in applications to continuum mechanics. The geometric content of the theory and the distinction between matrices and tensors are emphasized, and absolute- and component-notation are both employed. While the mathematics is rigorous, the style is casual. Chapter 1 deals with the basic notion of a linear vector space; many examples of such spaces are given, including infinite-dimensional ones. The idea of a linear transformation of a vector space into itself is introduced and explored in Chapter 2. Chapter 3 deals with linear transformations on finite dimensional real Euclidean spaces (i.e., Cartesian tensors), focusing on symmetric tensors, orthogonal tensors, and the interaction of both in the kinetically important polar decomposition theorem. Chapter 4 exploits the ideas introduced in the first three chapters in order to construct the theory of tensors of rank four, which are important in continuum mechanics. Finally, Chapter 5 concentrates on applications of the earlier material to the kinematics of continua, to the notion of isotropic materials, to the concept of scalar invariant functions of tensors, and to linear dynamical systems. Exercises and problems of varying degrees of difficulty are included at the end of each chapter. Two appendices further enhance the text: the first is a short list of mathematical results that students should already be familiar with, and the second contains worked out solutions to almost all of the problems. Offering many unusual examples and applications, Linear Vector Spaces and Cartesian Tensors serves as an excellent text for advanced undergraduate or first year graduate courses in engineering mathematics and mechanics. Its clear writing style also makes this work useful as a self-study guide.
Introduction to Applied Linear Algebra
Title | Introduction to Applied Linear Algebra PDF eBook |
Author | Stephen Boyd |
Publisher | Cambridge University Press |
Pages | 477 |
Release | 2018-06-07 |
Genre | Business & Economics |
ISBN | 1316518965 |
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
A Vector Space Approach to Geometry
Title | A Vector Space Approach to Geometry PDF eBook |
Author | Melvin Hausner |
Publisher | Courier Dover Publications |
Pages | 417 |
Release | 2018-10-17 |
Genre | Mathematics |
ISBN | 0486835391 |
A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.
Circuits, Matrices and Linear Vector Spaces
Title | Circuits, Matrices and Linear Vector Spaces PDF eBook |
Author | Lawrence P. Huelsman |
Publisher | Courier Corporation |
Pages | 306 |
Release | 2013-08-16 |
Genre | Technology & Engineering |
ISBN | 0486280446 |
This high-level text explains the mathematics behind basic circuit theory. It covers matrix algebra, the basic theory of n-dimensional spaces, and applications to linear systems. Numerous problems. 1963 edition.
Linear Algebra
Title | Linear Algebra PDF eBook |
Author | Alan Tucker |
Publisher | Macmillan College |
Pages | 472 |
Release | 1993 |
Genre | Mathematics |
ISBN |
Covers the fundamental role of linear algebra with both pure and applied mathematics as well as client disciplines such as engineering, the physical sciences and economics. This text examines the interrelationships amongst theory, computation and applications.