Linear algebra done right
Learners exploring linear algebra after 3Blue1Brown’s videos weigh a wide range of textbooks, from Strang’s matrix- and applications-first approach to Axler’s proof-heavy, abstract “second course,” along with alternatives like Treil, Boyd & Vandenberghe, Lay, and others. Commenters emphasize matching the book to the reader’s goals and background—engineering vs. pure math, first exposure vs. second pass, intuition vs. rigor—and debate Axler’s anti-determinant stance and the practicality of theory-heavy texts. Many recommend pairing a chosen book with video lectures, computer algebra systems, or interactive coding exercises to build both conceptual understanding and computational fluency.
Position of “Linear Algebra Done Right” (LADR)
- Commonly viewed as a second-course or “honors-style” book, emphasizing proofs and abstraction.
- Praised for clarity, structure, and especially its exercises, which many find challenging and conceptually unifying.
- Several commenters say it transformed how they “think in linear algebra.”
- Others found it dense, pretentious, or unusable as a first exposure; one person literally discarded it.
Comparisons with Other Books & Courses
- A more computation- and matrix-first text is often recommended as a first course, especially for engineers or those who liked visual/intuition-heavy video series.
- Some strongly prefer such an approach; others found it “impenetrable” and consider LADR simpler and more lucid.
- Other recommended texts span:
- Introductory, computation + theory mixes for beginners.
- More applied/real-world focused books with coding exercises (e.g., for ML, graphics, data).
- More abstract / proof-heavy texts for upper-division or graduate students.
- Opinions on specific books diverge widely; what works appears highly dependent on background and learning style.
Determinants Debate
- LADR’s de-emphasis and critical stance on determinants is a major flashpoint.
- Critics call this polemic misguided and distracting; they see determinants as central and geometrically intuitive (volume scaling, invertibility, composition).
- Defenders argue determinants are hard to motivate conceptually, often confuse beginners, and are better delayed until more structure (e.g., exterior products) is in place.
Pedagogy, Difficulty, and Learning Strategy
- Some educators dislike both the main “famous” intro texts for a first course, preferring more structured, beginner-friendly ones.
- Others say linear algebra is one of the easiest areas of math; many counter that it is harder than calculus initially due to abstraction.
- Strong push for:
- Pairing texts with lecture videos.
- Using computer algebra systems and numerical linear algebra resources.
- Self-teaching with “hand-holdy” books plus LLMs for clarification.
- Interactive coding (e.g., in Haskell/Lean) to build intuition.
Meta-Observations About Linear Algebra
- Several note linear algebra is not a single coherent narrative like calculus; it has multiple “centers”: computation, geometry, abstraction, and algebra.
- No consensus on a single “done right” approach; different books optimize for different goals and audiences.