マンガでわかる線形代数

マンガでわかる [Manga de Wakaru]

by Shin Takahashi, 高橋信, Iroha Inoue

※この電子書籍は紙版書籍のページデザインで制作した固定レイアウトです。

線形代数をマンガとわかりやすい解説で理解できる!!
本書は「マンガでわかる」シリーズの一冊として線形代数をとり上げる。主人公が難しいことをセリフで言っているだけではないスタイルのマンガと補足の文章および例題により、学部1年生程度の読者を想定して線形代数の基礎を理解させる。行列やベクトルの計算だけでなく、本来の線形代数の肝である線形空間や線形写像、固有値、固有ベクトルについてもきちんと解説する。

序章　押忍！ 線形代数
第1章　線形代数とは
1. 線形代数
2. 学問として重要な単元とテストに出題される単元
3. 数学者から見た線形代数
　3.1　数学者から見た線形代数
　3.2　線形代数と公理
第2章　基礎知識
1. 数の分類
2. 必要十分条件
　2.1　命題
　2.2　必要条件と十分条件
　2.3　必要十分条件
3. 集合
　3.1　集合
　3.2　集合の表記
　3.3　部分集合
4. 写像
　4.1　写像
　4.2　像
　4.3　値域と定義域
　4.4　全射と単射と全単射
　4.5　逆写像
　4.6　線形写像
5. ギリシャ文字
6. 理系特有の言回し
7. 組み合わせと順列
8. 主将の命令と写像
第3章　行列
1. 行列
2. 行列の計算
3. 特別な行列
第4章　行列（続）
1. 逆行列
2. 逆行列の求め方
3. 行列式
4. 行列式の値の求め方
5. 余因子を利用する方法で逆行列を求める
　5.1　第(I, j) 小行列式
　5.2　第(I, j) 余因子
　5.3　余因子を利用する方法で逆行列を求める
6. クラメールの公式で連立1 次方程式を解く
第5章　ベクトル
1. ベクトル
2. ベクトルの計算
3. ベクトルによる表現
第6章　ベクトル（続）
1. 線形独立
2. 基底
3. 次元
　3.1　部分空間
　3.2　基底と次元
4. 座標
第7章　線形写像
1. 線形写像
2. 何のために線形写像を勉強するのか
3. 特別な線形写像
　3.1　拡大
　3.2　回転
　3.3　平行移動
　3.4　透視投影
4. 核と像空間と次元定理
5. ランク
　5.1　ランク
　5.2　ランクの求め方
6. 線形写像と行列の関係
第8章　固有値と固有ベクトル
1. 固有値と固有ベクトル
2. 固有値と固有ベクトルの求め方
3. n 次正方行列のp 乗の求め方
4. 重解の存在と対角化
　4.1　重解が存在する場合の表現可能例
　4.2　重解が存在する場合の表現不可能例
付録1　練習問題
参考文献
索引
以下、ダウンロード
付録2　内積
1. 内積
　1.1　長さ
　1.2　内積
　1.3　なす角
　1.4　数学者から見た内積
2. 正規直交基底
　付録3　外積
1. 外積
2. 外積と平行四辺形
3. 外積と内積
　付録4　行列式の性質

Genres: Mathematics, Manga, Science, Nonfiction, Comics, Graphic Novels, Textbooks

263 pages, Tankobon Hardcover

First published November 1, 2008

About the author

高橋信

Reviews

[Martin · Rating 5 out of 5]

This book shows why karate and linear algebra could be important in your life.

[Rahul · Rating 4 out of 5]

A good beginner's manga guide to linear algebra with a sweet love story.

[Adeel · Rating 5 out of 5]

Completed the book couldn't grasp some basic concepts because I am mathematically unfit. Book was good though has reignited my interest in maths.

[J. Nic Fisk · Rating 4 out of 5]

Surprisingly a really good guide. I tend to only keep 1 reference per subject and this is it for Linear algebra. Won't replace a class or anything, but enough to piece together the subject when you need it.

[Timothy Deng · Rating 5 out of 5]

Charming plot, if a little obvious! Great explanation on the differences between bases and linear independence. One of the most valuable things I learned in here was finding the inverse of a matrix without using the terrible cofactor method they teach in school. The explanations on linear transformations and eigenvalues/eigenvectors helped me understand their meaning better conceptually, though I do wish there was more time spent on those two topics in particular.

[Beth G · Rating 4 out of 5]

Cute manga! This would be a nice supplement to any traditional linear algebra textbook. Most of the math is presented in manga format as we follow one character tutoring another, though some pages at the ends of chapters show solved problems to illustrate concepts.

As for the storyline - well, this book was written by and for math nerds, so you can wager your own guess as to whether our geeky protagonist wins the heart of the girl he likes. 🤓

[Nathan Albright · Rating 5 out of 5]

After having read this book and finding it greatly enjoyable as well as informative, I think that the Manga guides to other subjects are likely to be of interest to me as well.  By putting a layer between the admittedly somewhat dry and dull material of linear algebra and the reader, the book allows the reader to put themselves in the shoes of Misa, an appealing young woman who struggles with the subject and wants to know how practical it is and how to understand the material for her college math class.  And looking at this book as an entrance into the series as a whole, it is worthwhile to add one layer between the reader and the raw material of mathematics (or science), given that the interest in the plot itself allows the material to be more interesting because of the context that it is in.  It is only a wonder that this sort of approach has not been taken before because of its obvious appeal for those who are interested in both manga as well as math and science and who seek to leverage narrative and story to make mathematics and science easier to appreciate

At its core, this is a book that deals with three people with complex motivations.  We have Reiji, a freshman at a university who is a bit of a weakling but devoted to getting stronger through the mastery of karate.  We have Tetsuo, who is powerful at karate but (spoiler alert) not too bright when it comes to math, and we have Tetsuo's younger sister Misa, a beautiful freshman girl who Reiji tutors in mathematics thanks to a deal he makes with Tetsuo.  The frame story of their interactions, and the growing attraction that Reiji and Misa feel for each other, as well as Reiji's attempts to prove himself to be strong takes place in the midst of instruction about linear algebra, where Reiji gives Misa (and the reader) various instruction on linear algebra in eight chapters, starting with an overview of linear algebra (1), moving on to the fundamentals of implication, equivalence, set theory, functions, combinations, and permutations (2), an introduction to matrices, matrix calculations, and special matrices (3), more matrices, including determinants and Cramer's rule (4), vectors and vector calculations (5), linear independence, bases, dimensions, and coordinates (6), linear transformations and matrix rank (7), and eigenvalues and eigenvectors (8).  The instruction fits snugly with the story of karate and romance that surrounds it and makes for a compelling vehicle for mathematics instruction and its practicality.

What does one get out of this particular book?  It is a compelling mixture of technical material, which is deadly dull when one looks at it on its own, with a fascinating story and beautiful artwork.  And that combination is one that would likely translate to a lot of other materials as well.  This book, and the series it belongs to, is evidence of at least a few things, namely the importance of learning math and science and the difficulty many people in learning the material and sustaining interest in it unless it is packaged in the right way.  Some people might be offended by this sort of thing, but as someone who finds it more worthwhile to learn and to encourage learning than to complain about the sort of form that the learning is bundled with, I don't see any reason to complain personally, except to wish that these had been around earlier.  Still, the story itself demonstrates the relationship between math knowledge and other skills, and demonstrates how it is that nerdy people can leverage their willingness to work hard at difficult subjects beyond math and science alone, which is useful information even for those who know the material already.

[Axel · Rating 5 out of 5]

This book was actually a great complement to my studies of linear algebra at university. I first came across it when I was in high-school, but linear algebra was overkill for what I studied at the time so I didn't put too much focus into it. But then I had a course in linear algebra at university, and thought back of this book. And it certainly helped me understand some of the concepts much better,

In my opinion the book can't single-handily help you understand everything about linear algebra. It works great as a complement though, especially if you find other literature on the subject boring or tedious.

[Venkatesh-Prasad · Rating 5 out of 5]

An accessible introduction to basics of linear algebra provided you are comfortable with basic algebra and matrix. The number of examples and visual illustration is the biggest pluses of the book. At times, I wished the author would elaborate the statements, e.g., minimality of basis.

The "comic book" aspect did not make a huge difference for me; may be, it would for high schoolers or eager middle schoolers.

All said, it provides an easy and quick refresher on linear algebra. It would make a great gift for high schoolers or eager middle schoolers :)

[Dorum · Rating 2 out of 5]

The concepts are explained in a relatively simple manner, most of them at least but:

1) The background story sucks. It is bland and has nothing to do with linear algebra.
2) The explanations are no different from any decent manual of basic linear algebra.
3) The authors takes what I would call a "cop-out". Whenever some more difficult concepts have to be explained, he skips the manga and simply makes long pages of text.

This three points really ruined it for me. I think Linear Algebra Done Right is a much better introduction to the subject.

[Uncertainty · Rating 4 out of 5]

Great book as introductory material to Linear Algebra, the book caught my attention from the very first pages I have skimmed through, entertaining, and it was an easy read.
I have incorporated using some LLMs and KhanAcademy to get more help and get answer of some questions about linear algebra.
That was my first book in this series of *Mangua Guide to*, and my next one will be *Mangua Guide to statistics*, and I won't stop there.

[Christina · Rating 4 out of 5]

A great refresh of linear algebra as my career has taken a turn into data science and machine learning algorithms. It was also exciting to see my local library had this and several others in the series (some of which I also took home) as they are a fun way to interact with complex mathematical concepts!

[Haydngoseek · Rating 4 out of 5]

A solid refresher of linear algebra fundamentals, which would make a decent introduction as well. The explanations are written/translated in a clear style, and the example problems are easy to follow. Would be nice if some of the denser textbook parts were interwoven more into the story, but there's really nothing else like it out there.

[Mahin · Rating 4 out of 5]

A sweet little semi technical book on Linear Algebra. You get to learn Linear Algebra with the cute background story of Misa and Yurino. Its not good enough as a standalone Introduction on the subject, but would be a decent supplement. I wanted to give it 3 stars, but had to give it 4 because of the cute romantic story of Misa and Yurino. :D

[Sami · Rating 4 out of 5]

Linear Algebra is a difficult topic to explain, but the author did very well! Sometimes I felt it should have explained the theoretics and key vocabulary a little more but that's minor. In all, this was a great introduction into Linear Algebra and the background story plot was adorable!

Generalized content warnings: None

[Johan · Rating 2 out of 5]

I really enjoyed the databases and universe manga guides, but this one was a tough nut to crack. I studied linear algebra little over half a life ago, but most of it didn’t ring a bell and I found it hard to understand what is was about. Weird. Will try another one.

[Sharanya · Rating 3 out of 5]

A good beginners guide , however would have preferred if some of the complex topics like bases , Eigen vectors were given the same set of treatment and importance as some of the other topics earlier in the book

[N. · Rating 3 out of 5]

This was an interesting library borrow. Thanks mate.

I needed help with algebra, but this was not quite what I needed. Still, it was an interesting basics guide with a manga framing story.

I'm going to keep an eye out for other stuff to research.

[Chris Shen · Rating 4 out of 5]

This book serves as an intro to basic procedures in linear algebra and can do good as a pre prep given that the exercises are done on paper alongside the book. I can also serve as a refresher after being familiar with some linear algebra experience.

[Chandra Prakash · Rating 5 out of 5]

This book is awesome, I really enjoyed reading this book. The way ideas are presented its quite good.

[Wattanit Hotrakool · Rating 4 out of 5]

Interesting delivery of a serious topic. The maths details are surprisingly deep — more of a university-level rather than a high-school level.

[Harinee · Rating 5 out of 5]

Absolutely Brilliant. Wish people wrote books like these to simplify subjects.

[E. · Rating 5 out of 5]

Better than my coursebook

[z · Rating 5 out of 5]

Absolute masterpiece

[Div K · Rating 5 out of 5]

Highly entertaining and educational

[Kushagra Tripathi · Rating 4 out of 5]

nice book to update basic linear algebra through comic visuals and stories

[Derek Kyan · Rating 5 out of 5]

A really good intro to linear algebra and a creative twist to teaching it through manga.

[Maxi · Rating 5 out of 5]

I read it for the plot.

[Alaa Ranga · Rating 4 out of 5]

5/5 for concept
4/5 for novelty
3/5 for execution

[Jonathan · Rating 3 out of 5]

Engaging but fairly shallow and scant on real world examples.