Intuitively Understand the Basics of Linear Algebra with Abundant Diagrams! Publication of 'Illustrated Linear Algebra: The Strang Method for Intuitive Understanding'

Kindai Kagaku Sha Co., Ltd., which operates a specialized book publishing business in the science and engineering fields under the Impress Group, announced the release of the book "Illustrated Linear Algebra" (Author: Kenji Hiranabe) from its Kindai Kagaku Sha Digital label (*) on April 22, 2026.

*What is Kindai Kagaku Sha Digital: It is an on-demand publishing label utilizing digital technology, where Kindai Kagaku Sha collaborates with authors in a project-based style. Please also see here for details.

https://www.kindaikagaku.co.jp/kdd/scheme/

● Bibliographic Information

[Title] Illustrated Linear Algebra

[Author] Kenji Hiranabe

[Specifications] A5 size, regular binding, partially color in print / partially color in digital, 274 main pages

[Standard Price (Print)] 3,300 yen (excluding tax)

[Standard Price (Digital)] 3,300 yen (excluding tax)

[ISBN] (Book with cover) 978-4-7649-0785-0 C3041

[ISBN] (POD) 978-4-7649-6140-1 C3041

[Product URL] https://www.kindaikagaku.co.jp/book_list/detail/9784764961401/

● Content Introduction

This book is an introductory text that aims for readers to intuitively master the essence of linear algebra, centering on the three elements of head (theory), hands (calculation), and eyes (illustration). The core of this book consists of the "4 subspaces" serving as a map overlooking the world of linear algebra, and the "5 matrix decompositions (LU, CR, QR, Eigenvalue, and Singular Value Decomposition)" which are extremely important in practice. In each chapter, the book starts with concrete example problems, interweaving detailed explanations of theorems with intuitive visual commentaries, structured so readers can steadily step up. In particular, the CR decomposition that vividly unravels the properties of a matrix's rank, and the Singular Value Decomposition (SVD) that serves as the foundation of modern machine learning and data science, are positioned as the highlights of the book, offering an "Aha! experience" where the knowledge learned through reading the entire book connects into a unified whole. Inspired by interactions with the renowned MIT professor Dr. Gilbert Strang, the diagrams in this book bring new discoveries and a deep sense of conviction to linear algebra.

● Author Introduction

Kenji Hiranabe

1989 Graduated from the Faculty of Engineering, The University of Tokyo

1989 Engaged in 3D CAD development at NKK Nippon Kokan (currently JFE Holdings)

1995 Made a U-turn to Fukui, joined Eiwa System Management, Inc.

2006 Established Change Vision, Inc. (astah*), President (current)

2009 Executive Committee Chair of Agile Japan

2015 President of Eiwa System Management, Inc. (current)

2018 Established Scrum Inc. Japan, Board of Directors (current)

While striving to popularize Agile domestically and internationally, he develops the UML editor software astah.

He believes in making software development more collaborative, creative, and above all, enjoyable.

Authored Books include:

"Agile Development and Scrum"

"Mind Maps Useful for Software Development"

Translated Books include:

"XP Extreme Programming Explained"

"The Essence of Lean Software Development"

"Agile Project Management"

"World Standard MIT Textbook Strang: Liberal Arts Linear Algebra"

and many others.

● Table of Contents

Chapter 1 Numerical Vectors and Matrices

1.1 Numbers and Vectors

1.2 Matrices

Chapter 2 Matrix Calculations Seen Through Diagrams

2.1 Vectors

2.2 Matrices

2.3 Special Matrices

Chapter 3 Subspaces and Linear Transformations

3.1 Subspaces and Bases

3.2 Linear Transformations

Chapter 4 LU Decomposition and Simultaneous Linear Equations

4.1 Gaussian Elimination

4.2 LU Decomposition

4.3 Row Echelon Form and Rank

Chapter 5 CR Decomposition and the 4 Subspaces

5.1 Matrix Rank and CR Decomposition

5.2 The 4 Subspaces

5.3 Existence and Uniqueness of Solutions for Simultaneous Linear Equations

Chapter 6 QR Decomposition and Projections

6.1 Projections

6.2 QR Decomposition and Projection Matrices

6.3 The 4 Subspaces and Projections

6.4 Properties of Projection Matrices

6.5 Orthogonal Matrices

6.6 Applications in Data Analysis

Chapter 7 Eigenvalue Decomposition XAX^-1

7.1 Determinants

7.2 Eigenvalues and Eigenvectors

7.3 Symmetric Matrices

7.4 Similarity Transformations

7.5 Positive Definite Matrices

7.6 Diagonalization, Triangularization, Spectral Decomposition

7.7 Real Matrices and Complex Matrices

7.8 Applications to Sequences and Differential Equations

Chapter 8 Singular Value Decomposition U∑V^T

8.1 Singular Value Decomposition (The Most Useful Decomposition)

8.2 Singular Values and Singular Vectors

8.3 Pseudo-Inverse Matrices

8.4 Dimensionality Reduction via Singular Value Decomposition

8.5 Applications in Statistics and Data Analysis

Appendix A The Breadth of Linear Algebra

A.1 World Map of Matrices

A.2 Letters and Names of Matrices

A.3 Function Spaces as Vector Spaces