Here's 3 amazing resources to learn Linear algebra:
Linear Algebra MIT course (ocw.mit.edu)
free • course • by Gilbert Strang • 2010
This is a basic course on matrix theory and linear algebra with emphasis on topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Some may find the presentation style too informal, but these lectures are superb for building geometric intuition and seeing the beauty and usefulness of linear algebra.
Linear Algebra: A Modern Introduction 4th edition (www.amazon.com)
paid • book • by David Poole • 2014
This textbook is a comprehensive introduction to all major linear algebra topics including vectors, matrices, systems of linear equations, eigenvalues and eigenvectors, vector spaces, and inner product spaces. It explains the concepts in plain English but also provides excellent geometric interpretations with pictures and rigorous proofs. A key feature is numerous examples on how linear algebra concepts are applied to solving problems in applied mathematics, physics, computer science, and other fields. If you want to pick up just one book to learn linear algebra, this textbook with over 2000 exercises is a perfect choice.
Linear Algebra Done Right, 3rd edition (link.springer.com)
paid • book • by Sheldon Axler • 2014
This textbook is a concise, clearly presented algebraic take on the subject. It gives little attention to the geometric and numerical sides of linear algebra and instead focuses on abstract vector spaces and linear maps. It assumes no prior knowledge, but it will be best as your second exposure to linear algebra.