To What Extent Should Computer Science Majors Master Linear Algebra

If you plan to focus solely on software development and working with databases, there is no need to study linear algebra in depth; passing the exams and earning the credits will suffice. However, if your future career plans might involve 3D vision, artificial intelligence, machine learning, or similar fields, a deep understanding of linear algebra becomes essential.

For example, in 3D transformations, if you are familiar with vectors and matrix transformations, you can basically understand the code at a glance. The code that seems complex is, in fact, just matrix operations.

If your future work might involve machine learning, linear algebra is even more critical. The currently popular AI architecture, the Transformer, is essentially large-scale matrix multiplication combined with nonlinear functions (also called activation functions).

I recommend the book Introduction to Linear Algebra by Gilbert Strang, who is an applied mathematician and a professor at MIT with 50 years of teaching experience in linear algebra. His linear algebra course is a classic and is featured by many platforms as a recommended course. His lecture videos can be found on platforms like Bilibili and NetEase Open Courses. This book is not as abstract as pure mathematics textbooks, nor does it focus solely on problem-solving drills. Instead, it truly helps you understand the concepts of linear algebra — vectors, spaces, and the meaning of matrix transformations. It is one of the best books for engineering students starting out in linear algebra, especially if you might work in AI-related fields in the future. If you thoroughly grasp this book’s content, you will be able to barely understand cutting-edge machine learning research papers. The author has written a total of 12 books, and this one is the most popular. The first edition was published in 1993, and the latest edition, the sixth, was released in 2023. This book is also very suitable for self-study; many students who have used it recommend combining the book with the author’s video lectures for a better learning experience.