『Volume 4.
Linear Algebra

PART 0.
Basic knowledge

0-1.
Sets and Propositions
0-2.
calculation
0-3.
simultaneous equations
0-4.
thought

PART I.
procession

1-1.
Meaning of matrix
1-2.
Matrix shape
1-3.
Matrix operations
1-4.
Various matrices
1-5.
Diagonal sum and determinant
1-6.
Inverse matrix
1-7.
Matrices and systems of linear equations
1-8.
Least squares solution

PART II.
Vector theory

2-1.
vector
2-2.
Components of a vector
2-3.
Dot product of vectors
2-4.
Cross product of vectors
2-5.
domain of vectors
2-6.
Equation of the plane
2-7.
Equation of a space line

PART III.
vector space

3-1.
vector space
3-2.
Basis and dimension of vector space
3-3.
space of the matrix
3-4.
Orthogonal projection vector

PART IV.
Eigenvalues ​​and eigenvectors

4-1.
Eigenvalue
4-2.
Eigenvector
4-3.
Properties of eigenvalues ​​and eigenvectors
4-4.
Diagonalization of a matrix
4-5.
Orthogonal matrices and orthogonal diagonalization

PART V.
linear mapping

5-1.
linear mapping
5-2.
Nucleus and top
5-3.
Sea space and commercial space
5-4.
Dimensions of nuclear and terrestrial boundaries
5-5.
Injective, surjective, and bijective morphisms
5-6.
Eigenvalues ​​of linear mappings
5-7.
Geometric interpretation of linear mapping

[supplement]
1. QR code decomposition
2.
Singular Value Decomposition (SVD)
3.
Complex Matrices [Introduction]
4.
Block matrix [Introduction]
5.
Idempotent and zero-power matrices

Practice Problem Answers and Explanations

[Book Review]

Kim X-do (Dokpyeonsa nickname: Nenyaple) - Yonsei University Department of Mathematics -
I would also recommend this book to beginners who have no knowledge of college mathematics.
Unlike other transfer math books, the author's efforts to provide intuitive and easy-to-remember explanations and many analogies are clearly evident, and this is a rare book that introduces both standard and practical solutions to problems that can be used on actual transfer exams.
Although this book is primarily intended for transfer exam preparation, I believe it will also be helpful for students who transfer to college and take calculus or engineering mathematics classes alongside their school textbooks to get good grades.

Kim X-ram - Dongguk University Mathematics Education/Pedagogy -
This book is not a simple listing of mathematical knowledge, but rather explores the logical structure between college mathematics concepts.
We have improved the efficiency and effectiveness of knowledge transfer through language that beginners can understand.
I would like to recommend this to students who want to learn college mathematics in a thorough and easy way.

Jeong X-yeol - Hanyang University College of Engineering -
If you are looking for a suitable self-study book for transfer math, I would definitely recommend "Science and Engineering Transfer Math 3.0."
Transfer mathematics, by its nature, requires you to acquire only the necessary information in a short period of time, but it covers the entire content of college mathematics, making it somewhat difficult to study.
For this reason, there are not many transfer math reference books published on the market.
I am confident that this book will be a ray of hope, relieving students of their worries, as it contains only the essential information needed for the exam.

Cho X-won - Seoul National University of Science and Technology, College of Engineering -
This book clearly explains the concepts to those who are studying transfer mathematics for the first time.
If you look at the math books on the market, you can see that they are simply a copy of the original text's proofs and formulas.
It's like, 'Either figure it out on your own or memorize the formula and try to solve it.'
On the other hand, 《Science and Engineering Transfer Mathematics 3.0》 is not a simple list of concepts, but rather solves problems and provides easy-to-understand explanations of why and in what situations the concepts should be used.
It felt like a commentary on a concept book.

[Successful Candidate Reviews]

"I solved almost all of my math problems with the science and engineering transfer math book.
It's a very well-made book."
Excerpt from the Success Story - One Successful Applicant to the Department of Electrical and Electronic Engineering at Sungkyunkwan University

"It was easy to study because the core concepts of transfer mathematics were explained in an easy-to-understand manner.
For those who are just starting to study transfer math, I recommend starting with this book."
Excerpt from "Success Story - One Successful Candidate in Sogang University's Computer Engineering Program"

“It was very helpful to realize that there are different approaches to solving problems.
If it weren't for the science and engineering transfer math, I probably wouldn't have passed."
Excerpt from an Admissions Story - A Successful Applicant to the Department of Electrical and Electronic Engineering at Konkuk University