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Linear Algebra is not what it seems at first thought. Behind all the matrices, polynomials, vectors and spaces, there is a fascinating subject which tools can help you to solve many practical problems. Linear Algebra is a topic connected to different fields inside and outside mathematics like functional analysis, differential equations, engineering, graph theory, statistics, linear programming, and computer graphics.
Its study is essential in most degree courses, especially those related to engineering or science. To show a simple example, it is impossible to develop graphic software applications like photo editors or graphical games without a good understanding of this topic.
There are hundreds of books with the aim of teaching Linear Algebra, your choice will depend, basically, on the kind of course you are taking, and on the approach, prose and rigor of the text you prefer to study. Here I propose a brief list of books, based on my personal experience, from famous books I have read or consulted. The order used to present the books is not relevant. I hope this list can help you to decide which book is the best for you.
An excellent linear algebra textbook, with a good introduction. It is written in a clear way with lots of interesting examples and very good exercises. In every chapter the author gives a good concrete foundation before introducing the more abstract concepts.
In order to enable students to visualize and understand complex concepts, as well as the meaning of the calculations that they will encounter, the author introduces, from the first moment, the concepts of vectors and vector geometry, emphasizing on geometric intuition. He also prepares students to make the transition from the computational aspects of the course to the theoretical; by giving an abundant selection of applications from a broad range of disciplines that clearly demonstrates the relevance of linear algebra.
One of the best introductions to linear algebra, just fantastic! It is a full presentation that will give you an intuitive grasp of linear algebra from both, the geometric and algebraic points of view, and will capture your attention until the end of the book. A variety of interesting examples and exercises in each chapter will help you to understand and manipulate the objects of linear algebra.
The novel approach taken in this book banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces, which are more abstract and more general than matrices themselves, while providing easy proofs of theorems.
A well organized, well explained, and well written book. It’s written in a very didactical way, so it’s suitable for self-study. Concepts are explained clearly and concisely, highlighting the key information, and presenting useful examples. On each section, the author presents a brief, but useful discussion on real world applications. The text also includes several exercises, which seem perfectly targeted for each section.
The author introduces Linear Algebra concepts early in a familiar, concrete R^{n} setting, develops them gradually, and returns to them again and again throughout the text so that when discuss in the abstract, these concepts are more accessible.
This is a practical, problem-oriented textbook, especially valuable for a computational perspective. Its most distinctive feature is a seamless integration of the theoretical, computational, and applied aspects of the subject, which stems from the author's extensive experience in both teaching and research. The author manages to explain complex topics in a manner, understandable to an undergrad, without simplifying or skipping parts. He is patient and thorough and explains even the simpler issues step by step. He takes his time to make sure that everything is crystal clear.
Some of the more contemporary topics of applied linear algebra are included in the text, which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a large number of carefully chosen exercises from which the students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms.
The organization of the book is also excellent and it manages to maintain a perfect coherence between sections while each chapter can be read alone as well.
This book is designed for an introductory course in matrix and linear algebra; offering a fresh approach to those topics by providing a balanced blend of all three of the basic components of linear algebra: applications, theory, and computation, which gives students the tools they need as well as the motivation to acquire these tools. Each section ends with a set of exercises where students must prove their acquired knowledge.
The book places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects, focusing on numerical computation and applied mathematics, which means that matrix analysis plays a central role. Throughout the book, significant motivating examples are woven into the text, which help students to appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this book will also teach students how concepts of matrix and linear algebra make concrete problems workable.
This book is intended for the first course in linear algebra, the level is not rigorous, but its pedagogical approach makes it perfect to introduce this subject. This classical book balances mathematical techniques and mathematical proofs. It presents theory in small steps and provides more examples and exercises involving computations than abstract texts.
To demonstrate how linear algebra can be applied in different fields of science, the author presents several applications, and many examples and exercises make reference to different disciplines.
Gilbert Strang is a Professor of Mathematics at Massachusetts Institute of Technology, his lectures can be seen in YouTube, where you soon will notice his particular approach to teach Linear Algebra, which is also pervaded in this book. Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.
This textbook is intended for first courses in linear algebra. Instead of teaching students by repetitive drill, the author encourages students to real mathematical thinking; an approach that has been successful over many years at MIT.
The book includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, Fourier methods and the Fast Fourier Transform, linear programming, and computer graphics.
This book, also written by renowned professor Gilbert Strang, is an excellent and accessible intro to the subject, where the author begins with a brief and enthusiastic explanation of the nature of linear algebra.
The book is written in a very colloquial and natural way, using an informal and personal style, and emphasizing on understanding instead on proofs; nevertheless it does not flow as easily as the author’s lectures. The proposed problems, give you the opportunity to practice the theoretical as well as computational algebraic skills.
The author tries, in all moment, to demonstrate that linear algebra is a fascinating subject by showing both, its beauty and value. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics. He explains concepts, rather than deduces.
The book can be summarized as a very lovely, graceful, poetic examination of linear algebra from a very applied background.
Learning by examples is an approach that works for many students. This book contains 3000 Solved Problems that can not only help students to understand abstract concepts of linear algebra, but they are also, an excellent complement for any course of Linear Algebra. Solved problems cover from simple problems to proofs of theorems, which help you to organize the thought processes and give you a better concept and intuition of the material.
The book is very clear and complete, and the range of material covered is more than you will find in the lower undergraduate class. If you take the time to work through this book, you will be a master of the topic with a much wider foundation and with many different approaches to same problem. It will also help you catch up on the little "details" which you might have absorbed for the duration that you thought you would be tested on it, but after such time the information vanished into the void of forgotten math.
It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams, because it solves problems like those you'll find on your exams.
This famous book is designed for use as a textbook for a formal course in linear algebra or as a supplement to all current standard texts. Each chapter begins with clear statements of pertinent definitions, principles and theorems together with illustrative and other descriptive material. It’s easy-to-follow and all topics are well organized. It provides hundreds of examples, solved problems, and practice exercises to test the student’s skills.
The solved problems serve to illustrate and amplify the theory, bring into sharp focus those fine points without which the student continually feels himself on unsafe ground, and provide the repetition of basic principles so vital to effective learning. Numerous proofs of theorems are included among the solved problems. Supplementary problems serve as a complete review of the material of each chapter.
Its last editions include new problems relevant to computer science and examples that demonstrate the applicability to the fields in which linear algebra is now essential: computer science, engineering, mathematics, physics, and quantitative analysis.
From a pedagogical point of view, the book is excellent, and it will be found helpful to all readers regardless of their fields of specialization.
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