The choice of basically choosing the book depends on the kind of course you are taking and on the approach, prose and obduracy of the text you prefer to study.
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.
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.
Here are some books which are considered to be the BEST BOOKS FOR LINEAR ALGEBRA:
Theory and Problems of Linear Algebra
By Seymour Lipschutz
The beginning of chapters stars with clear statements of pertinent definitions, principles and theorems together with other descriptive material.
This whole book is in a flow, easy to follow and to study topics in a organized way.
Numerous proofs of theorems are included in the solved problems. Supplementary problems helps to review of the material of each chapter.
Last editions contains new problems which are relevant to computer science and there examples and also to the fields in which linear algebra is now essential: computer science, engineering, mathematics, physics, and quantitative analysis.
Linear Algebra: A Modern Introduction
By David Poole
The concepts of vectors and vector geometry, emphasizing on geometric intuition, meaning of calculations are properly explained. It prepares students to make the transition from the computational aspects of the course to the theoretical ones.
Linear Algebra Done Right
By Sheldon Axler
This is taken as the best experience for the Introduction to Linear Algebra, as it helps to solve both algebric and geometric points of view with interesting facts and examples.
The central goal of algebra: which is understanding the structure of linear operators on vector spaces is thoroughly focused till the end of the book .
Matrix Methods in Data Mining and Pattern Recognition, Second Edition
This second edition is revised numerical linear algebra techniques for solving problems in data mining and pattern recognition.
The author describes how modern matrix methods can be applied in real life scenarios which provides a set of tools to the students which can be modified later.
Linear Algebra and its Applications
By David C. Lay
This book is considered best for self -study and analysis. Key points are highlighted and abstracts are provided for every topic with given examples. Author provides real world applications also on each topic. Topic-based exercises are there to make the understanding better.
Linear algebra concepts are introduced early to make reader familiar and taken back gradually through text so that these concepts are more accessible .
Matrix Analysis and Applied Linear Algebra
By Carl. D. Meyer
This book is good for students in undergraduate as author’s research and experiments are clearly mentioned.
Topics are crystal clear and some contemporary topics are also explained which are not easily found in any other undergraduate course books.
This also carries a pack of historical notes with comments on numerical performance and the possible pitfalls of algorithms.
Each chapter can be read alone and in-between the topic explanations are also in coherence.
Glossary of Mathematical Terms and Concepts
Ram Bilas Misra
This served as a refrence book where the topics are arranged in alphabetical order.
First volume ~Algebra (Classical) and covering up to Geometry (3-dimensional Coordinate)
Second Volume~ Differential Geometry and Jacobians
Present Volume~ Laplace Transform up and Special Functions.
Applied Linear Algebra and Matrix Analysis
By Thomas S. Shores
This is considered as an fully-fledged tool book for Linear algebra as it contains it’s applications , theory and computation. Computer exercises and projects focusing on numerical computation and applied mathematics, plays a central role.
This also teaches how concepts of matrix and linear algebra makes hard problems easy to solve.
Elementary Linear Algebra with Applications
By Stanley I. Grossman
This can be used to make someone acquainted with the subject as intended for the first course in linear algebra.
Less theory with short steps are than expanded into more examples and explanations.
The author also provides the knowledge of how linear algebra can be applied into many other fields.
3000 Solved Problems in Linear Algebra
By Seymour Lipschutz
This book contains 3000 Solved Problems which can help students to understand
concepts of linear algebra.
Simple problems ranging from there proofs to topic-based exercises are also added by the author.
This can help an individual to become the master of any particular topic.
Introduction to Linear Algebra
By Gilbert Strang
This book has already been appreciated
as it includes differential equations, graph theories , statistics, Fourier methods and the Fast Fourier Transform, linear programming and computer graphics.
The author of the book Gilbert Strang is a Professor of Mathematics at Massachusetts Institute of Technology , his teaching videos can be seen on YouTube.
Students are encouraged to deal with real mathematical thinking.
Galois Theory and Advanced Linear Algebra
Key concepts like Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals are explained.
Advanced linear algebra with Galois theory including canonical forms are introduced which are divided into four chapters.
But yes, the book is written in a way where readers are expected to have a basic knowledge of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations.
Lectures on Abstract Algebra
Dr Michael K. Butler
This book belongs to the group of students who are persuing any undergraduate course having mathematics as a subject. All aspects that can be expected to encounter in undergraduate like ring theory, group theory and the beginnings of Galois theory are thoroughly explained.
It is already taken in mind that the reader have only the rogh knowledge of basics like complex numbers, matrices, and solving systems of linear equations after that it will take you eventually by expanding the broader perspective of the concepts including groups and structure-preserving mappings between objects such as homomorphisms of groups and linear transformations of vector spaces and also vector spaces and rings too.
The CONTENTS of books are mentioned here:
1 The Group Axioms and Examples
2 Subgroups and Group Homomorphisms 3 Vector Spaces
4 Subspaces and Linear Transformations 5 The Basis for a Vector Space
6 Eigenvalues and Eigenvectors
7 Inner Product Spaces
8 Cosets and Quotient Groups
9 Group Actions
10 Simple Groups
11 Soluble Groups
12 Fields and their Extensions
13 The Galois Group
14 The Ring Axioms and Examples
15 Subrings, Ideals and Ring Homomorphisms
16 Quotient Rings
17 Integral Domains and Fields
18 Finite Fields
19 Factorisation in an Integral Domain 20 Vector Spaces with Products
21 The Exterior Algebra of a Vector Space
22 Lie Algebras
23 Matrix Groups and their Tangent Spaces
24 Normed Real Algebras
25 Tensor Products and Clifford Algebras.
Linear Algebra and its applications
By Gilbert Strang
Book starts with the brief knowledge of the nature of linear algebra.
The beauty of this book is that, it is written in very casual and informal way just to enhance it’s understanding more.
The very renowned professor Gilbert Strang , who is also the author of this book tried to present linear algebra as an fascinating subject. He focuses on concepts, rather than directly jumping on the conclusions.
There are many good books in markets and shops out there. These are few which were suggested and I shortlisted them.
I hope you found this article helpful.