The Manga Guide to Linear Algebra

The latest in the Manga Guide series tackles the complicated math of Linear Algebra.

As with the other books, there’s a framing story to involve the reader and provide a sympathetic co-learner. Here, it echoes the classic shonen fight manga structure, as freshman Reiji wants to join the karate club. He’s too scrawny, though, so he strikes a deal with the brawny club captain — he will be allowed to join if he tutors the captain’s sister Misa in linear algebra. Of course, she’s adorable, but Reiji’s afraid of what her monster brother would do if he hit on her.

Also following the Manga Guide pattern, some chapters are followed by a text section with more depth. Not all of them, though — more of this book is in comic format than others in the series. The chapters here are paired. The first two explain what the subject is, involving transformations and functions, with the basics of set theory and logic brought up as a refresher. As always, the images are incredibly helpful in visualizing the examples and concepts.

Chapters three and four cover matrices; five and six, vectors. The final two chapters are the most complex, covering linear transformations (used in computer graphics), then eigenvalues and eigenvectors. Throughout, Reiji wins the reader over with his determination and good humor in both learning and teaching, despite pushing himself to the limit in learning karate. His story is familiar, which is comforting.

I appreciated the way the author tackled the question “what is linear algebra good for?” He admits, “It doesn’t stand that well on its own, to be completely honest” but states it’s an important foundational subject for mathematicians and physicists. There are sample pages and extra material at the publisher’s website. (The publisher provided a review copy.)


  1. Still don’t know why I needed linear algebra for a compsci degree.

    I got to put it towards a math minor, though.

    (Funnily enough, number theory — which was not a required course for my major and which I only took as an extra math credit toward a minor — was much more pertinent to compsci than nearly any of the actual required math courses, as it’s the basis for cryptography. Wonder if they’ve changed the major requirements since I graduated; it would make a lot more sense to require number theory than linear alg, calc, diffeq, etc.)

  2. Linear Algebra teaches about vectors and arrays, even if not in the exact form used by computers. But it is also the first math class in the traditional “Calculus Track” that deals with Discrete Math. Number Theory is a better way to learn it, but at many colleges NT is considered a Senior class.

    Considering how often Transition Matrices are used in Business, Sociology, Genetics, and a host of other fields, I find it odd that the author couldn’t find anything better to say than “Um, well, you need it for more Advanced Math.”

  3. Wait this actully teaches math!?!……Wow I think I should buy it …HUUMMM….*__*

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