Linear Algebra for Beginners | Best Books for Linear Algebra | How to study Linear algebra

Introduction: 

In our BSc 2nd or 3rd year, we Maths honours students encounter a new paper called Linear Algebra. And I think this is the most beautiful subject in undergraduate level in mathematics. If we study this subject in a proper way it becomes very very interesting to us and also for entrance examination for masters in different central universities, IIT JAM etc, a significant amount of questions comes from Linear Algebra which are very good for scoring. But most of the students got stuck due to not getting the actual flavour of linear algebra which is geometric interpretation and connections between the concepts. 

So in this blog I’ll try to give some ideas how can we learn linear algebra by self study, which are the books we should follow, some useful links for YouTube videos which will help us for geometrical visualisation of different concepts.

How to study Linear Algebra:

In linear algebra,(for beginners) we can have two approaches namely set theoretic and matrix approach. But the best way is to go with both of them parallelly because only then we can feel the beauty of linear algebra and connection between the concepts. 

In BSc, we start studying abstract mathematics, but if we find some geometrical interpretations then the concepts becomes easy to understand. The same happens in case of Linear algebra also. Before going to abstract setup we can see the beauty of different concepts by imagining or plotting in 2D or 3D space. 

So for that I’ll suggest two books in linear algebra which will be the best for self study:

 1. Linear algebra: A geometric approach , by S kumaresan.

 2. Linear algebra by Stephen H Friedberg.

First start with the book by S kumaresan which will give you a set theoretic flavour with geometric interpretations of different concepts. This book will give the best motivations for linear algebra. Once you complete first two or three chapters go through the following link, which will help you to visualising the concepts. Or you can just go first with the videos for motivation and then go through the books,but anyway you have to follow the Books to learn properly. 

https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

Second book I have mentioned is for learning the concepts parrallelly with both matrix and set theoretic approach. Once you got some comfort with the concepts from the first book you can start this book. The exercises in this book after each topic will help you for self evaluation also these exercises will help you to solving the questions from entrance examinations. The more you solve the problems, the more you will learn. And in linear algebra only understanding the concepts is not enough. For doing good in exam you have you solve a lot of problems because if you can’t solve problems then saying “i understood” is meaningless.

Once you get done with first three-four chapters from these two books then you can start solving previous years question paper for different entrance exams. And if can solve some problems it will automatically make yourself to fall in love with the subject.

Books for linear algebra for some advanced level:

 1. Linear algebra: A geometric approach , by S kumaresan.

This book is for absolute beginners, this will give you a set theoretic flavour with geometric interpretations.

 2. Linear algebra by Stephen H Friedberg.

This book will help you to understand how matrix played a important role in linear algebra and  from this book you will learn how the same concept can be approached from different perspective and you can relate different concepts.

3. Linear algebra done right by S axler.

You can also follow this for directly for self study.

4. Linear algebra by Hoffman and Kunze.

This book is for little advanced study in linear algebra. This book will help you to develop skills  in acquiring abstract concepts in linear algebra.

5. Matrix analysis by Horn and Johnson.

This book is actually for advanced study but you can follow the first two chapters from this book and see some beauty in how the this work in advanced level. Also first two chapters will summaries the first two bookS that I have mentioned.

YouTube links for study linear algebra:

1. https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

This playlist will help you to visualise the basic concepts in linear algebra geometrically.

2. https://www.youtube.com/playlist?list=PLbMVogVj5nJQ2vsW_hmyvVfO4GYWaaPp7

This playlist will help you to go through the topics in a organised way.

3. https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D

This playlist will help you to visualise and understand the concepts clearly and help you to relate the concepts.

That’s all for today. Start studying and start loving pure mathematics and please study mathematics like mathematics. If you have any questions please ask in the comment box or you can mail me or drop a message in Facebook. Please do share the vlog.

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N.B. This blog is for those students who also want to do some great work in mathematics but due to lack of guidance they lack somewhere behind. You can share this blog  because may be you don’t need this but there will be someone who feels he could do better if he get some guidance.