The following are some good books to own in the area of Linear Algebra.

Linear Algebra (2nd Edition)

This is the gold standard for linear algebra at an undergraduate level. This book has been around for quite sometime a great book to own.

Linear Algebra: A Modern Introduction

Good book if you want to learn more on the subject of linear algebra however typos in the text could be a problem.

Linear Algebra (Dover Books on Mathematics)

An excellent book to own if you are looking to get into, or want to understand linear algebra. Please keep in mind that you need to have some basic mathematical background before you can use this book.

Linear Algebra Done Right (Undergraduate Texts in Mathematics)

A great book that exposes the method of proof as it used in Linear Algebra. This book is not for the beginner though. You do need some prior knowledge of the basics at least. It would be a good add-on to an existing course you are doing in Linear Algebra.

Linear Algebra, 4th Edition

This is good book to own but its more a split level book. It has material an undergraduate would want but also spills over to the graduate level a bit.

Multilinear Algebra (Universitext)

Note, this is an advanced text for LA. Multilinear algebra extends LA.

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