Quick Answer: Introduction to Linear Algebra by Gilbert Strang is the most widely used linear algebra textbook at UK universities, backed by free MIT OpenCourseWare lectures viewed over 10 million times. It is the right choice for mathematics, engineering, computer science, and data science students.
Yes — Introduction to Linear Algebra by Gilbert Strang is the standard linear algebra text at many UK universities (Cambridge, Imperial, Edinburgh, Bath, Warwick) and is essential reading for maths, engineering, CS, and data science students. The accompanying free MIT lecture videos make it uniquely powerful as a self-study resource.
📋 In This Review
What Is Gilbert Strang’s Linear Algebra?
Introduction to Linear Algebra by Gilbert Strang is a first course in linear algebra aimed at undergraduates in mathematics, engineering, computer science, and the physical and social sciences. First published in 1993, it is now in its 6th edition (2023) and has become arguably the most famous linear algebra textbook in the world.
Professor Strang has taught linear algebra at MIT for over fifty years. His 18.06 course on MIT OpenCourseWare is one of the most-watched academic lecture series in history, with over 10 million views. The textbook and the lectures are designed to complement each other — together they form one of the most effective self-study resources available in any subject.
| Author: | Gilbert Strang, MIT |
| Current Edition: | 6th Edition (2023) |
| Publisher: | Wellesley-Cambridge Press |
| Free resources: | Full lecture series free on MIT OCW |
| Used at: | Cambridge, Imperial, Edinburgh, Bath, Warwick, UCL and many others |
| Best for: | Maths, engineering, CS, data science, machine learning |
What’s Inside
Vectors and Linear Equations — the book opens with vectors and systems of equations, building geometric intuition before introducing algebraic methods. The approach is direct and practical, unlike more abstract treatments.
Matrix Algebra and Factorisation — elimination and LU decomposition are developed carefully, explaining not just how but why. The four fundamental subspaces (column space, null space, row space, left null space) are a recurring theme throughout the book.
Orthogonality and Least Squares — projection, orthogonal bases, Gram-Schmidt, and least squares are covered thoroughly. This section is particularly important for statistics, machine learning, and signal processing applications.
Determinants and Eigenvalues — eigenvalues and eigenvectors receive extensive treatment, with applications to differential equations, Markov matrices, and dynamic systems.
Singular Value Decomposition (SVD) — one of Strang’s particular strengths is the SVD, which he regards as the pinnacle of linear algebra. The treatment is clear and motivating, with applications to data science and machine learning.
6th Edition: Optimisation and Learning from Data — the newest edition adds two chapters on optimisation and learning from data, making it particularly relevant for students in machine learning and AI programmes.
“I genuinely believe that watching Strang’s MIT lectures alongside reading this book is one of the best learning experiences available to any maths or CS student. The combination of visual intuition, clear exposition, and practical application is unmatched.”
— Hannah, Year 3 Mathematics, University of Bath
The Free MIT Lectures
🎓 Free Online Resource
The complete MIT 18.06 Linear Algebra course is available free on MIT OpenCourseWare — 34 video lectures, problem sets, and exams. This is one of the most valuable free educational resources in existence. The book and lectures are designed together; using both simultaneously is strongly recommended.
The free availability of the MIT lectures raises a genuine question: do you need to buy the book at all? The honest answer is yes — the lectures and the textbook serve different purposes. The lectures develop intuition and motivation; the book provides the problems, worked examples, and complete reference material that you need for exams and coursework. Most students find the combination of watching lectures before reading each chapter to be the most effective approach.
Which Edition to Buy
6th Edition (2023) — current. Adds chapters on optimisation and learning from data. If you are studying machine learning or data science, this edition is worth having for those chapters specifically.
5th Edition (2016) — still excellent. The core content covering vectors, matrices, eigenvalues, SVD, and the four subspaces is unchanged from the 5th to 6th edition. A used 5th edition is sufficient for standard linear algebra courses and costs considerably less. Check whether your university reading list specifies the 6th edition before buying.
Where to Buy It Cheapest
New 5th and 6th editions available. Check for used marketplace copies.
Check Price on Amazon →Used 5th edition copies available from £15–25. Best value for standard linear algebra courses.
Browse Used Copies →Axler’s Linear Algebra Done Right is available on SpringerLink — a strong alternative for pure maths students.
View on SpringerLink →Our Verdict
Essential — the most practical and accessible linear algebra textbook available
Introduction to Linear Algebra by Gilbert Strang is the standard choice for undergraduate linear algebra at UK universities, backed by the world’s best free lecture series. The combination of clear exposition, practical applications, and freely available video lectures makes it uniquely valuable. For maths, engineering, CS, and data science students, this is the book to buy.
Related: Best Maths Textbooks for UK First Year Students | Apostol vs Spivak Calculus — Which Is Better?
Is Gilbert Strang’s book good for beginners?
Yes — Introduction to Linear Algebra is designed for first courses in linear algebra. It builds from vectors and equations to abstract concepts gradually, with strong geometric intuition throughout. It is significantly more accessible than abstract algebra-first treatments like Axler’s Linear Algebra Done Right.
Do I need to buy the book if I watch the free MIT lectures?
Both are recommended. The MIT 18.06 lectures (free on OpenCourseWare) develop intuition and motivation; the textbook provides the problems, worked examples, and complete reference material needed for exams. Most students use both: watch lectures first, then read the corresponding book chapter.
Which edition of Strang should I buy?
The 6th edition (2023) adds chapters on optimisation and learning from data — worth having if you are studying machine learning or data science. The 5th edition (2016) covers all standard linear algebra content and a used copy is significantly cheaper. Check your university reading list before buying.
Is Strang better than Axler for UK university linear algebra?
They serve different purposes. Strang is applied and computational — ideal for engineering, CS, and data science. Axler’s Linear Algebra Done Right is more abstract and proof-based — better for pure mathematics students. Most UK linear algebra courses use Strang; check your course syllabus.
Last Updated: Last Updated: July 2026 | Author: Textbooks.co.uk Editorial Team
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