63070011 Linear AlgebraI

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School Liberal Arts Education Program

Lecture Code 63070011 Subject Classification Foundation Courses

Subject Name 線形代数学I[1情]

Subject Name
（Katakana）センケイダイスウガク１

Subject Name in
English Linear AlgebraI

Instructor NAGAHARA MASAAKI

Instructor
(Katakana) ナガハラ　マサアキ

Campus Higashi-Hiroshima Semester/Term 1st-Year, First Semester, 1Term

Days, Periods, and Classrooms (1T) Mon9-10,Fri9-10：IAS L102

Lesson Style Lecture Lesson Style
(More Details) Face-to-face, Online (simultaneous interactive), Online (on-demand)

Classes are primarily scheduled to be held in person. However, they may be switched to or combined with online (on-demand) sessions due to various circumstances. In such cases, the instructor will notify you through Momiji or other platforms.

Credits 2.0 Class Hours/Week 4 Language of Instruction J : Japanese

Course Level 1 : Undergraduate Introductory

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Matrices, Determinants, Systems of Linear Equations, Vectors, Linear Spaces, Eigenvalues

Special Subject for Teacher Education 　 Special Subject 　

Class Status within
Liberal Arts Education This course serves as pre-specialized education with organic links to specialized studies. It aims to provide students with the foundational knowledge necessary for their respective fields, enabling them to master the logical framework and systems of basic disciplines, as well as the essential knowledge and skills for academic development.
Expected Outcome The goal is for students to master the logical structure and systematic organization of the fundamental sciences in their respective subjects. By the end of the course, students will be able to articulate and explain the core knowledge and skills required for academic development.

Class Objectives
/Class Outline ## Course Objectives
In conjunction with "Linear Algebra II," this course aims to provide students with the fundamental knowledge and skills of linear algebra.
## Course Description
This course covers approximately the first half of the following topics in linear algebra:
- Matrix operations, regular matrices, and inverse matrices
- Elementary matrix transformations, systems of linear equations, and matrix rank
- Properties of determinants, determinant expansion, and Cramer's rule
- Linear spaces, linear independence, and dimension
- Linear maps, linear transformations, and orthogonal transformations
- Eigenvalues, eigenvectors, and diagonalization

Class Schedule [An Example of Class Schedule]
lesson1: Matrix, Vector and Calculation of Matrices
lesson2: Square Matrices and their Properties
lesson3: Block Matrices
lesson4: Simultaneous Linear Equations
lesson5: Gaussian Elimination and Rank
lesson6: Definition of Determinant
lesson7: Solution of Simultaneous Linear Equations
lesson8: Solution of Homogeneous Simultaneous Linear Equations
lesson9: Introduction to Determinant
lesson10: Permutations and their Properties
lesson11: Sign of Permutation
lesson12: Determinant and it basic Properties
lesson13: Properties of Determinant
lesson14: Laplace Expansion
lesson15: Determinant of Special Types of Matrices

Final Exam

Text/Reference
Books,etc. Gilbert Strang, Linear Algebra for Everyone, Wellesley-Cambridge Press, 2020.
(Japanese translation: Strang: Kyoyo no Senkei Daisū, translated by Kiminori Matsuzaki and Kenji Hiranabe, Kindai Kagakusha, 2023.)

PC or AV used in
Class,etc. Text, moodle

(More Details) Lecture slides will be distributed on Moodle after each class. Additionally, students are required to take review quizzes on Moodle to reinforce their understanding of the course content.

Learning techniques to be incorporated Quizzes/ Quiz format

Suggestions on
Preparation and
Review Please ensure that you purchase your own copy of the textbook and use it for both pre-class preparation and post-class review. To improve your skills, it is highly recommended that you solve the practice problems in the textbook for the sections covered in the lectures. While the solutions are in English, they are available at the following link:

https://math.mit.edu/~gs/linearalgebra/ila5/ila5sols.pdf

Requirements

Grading Method Please complete the review questions on Moodle after each lecture. Submission of these assignments will be used to record your attendance. Your final grade will be determined based on both attendance points and the results of the final examination.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message Each class includes a dedicated session for exercises. The goal is to establish a cycle of attending the lecture, working through problems independently, and verifying your results. By participating actively and keeping up with the coursework, you will have a solid grasp of fundamental linear algebra concepts by the time 1T concludes.

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2026Year	School/Graduate School	Liberal Arts Education Program
Lecture Code	63070011	Subject Classification	Foundation Courses
Subject Name	線形代数学I[1情]
Subject Name （Katakana）	センケイダイスウガク１
Subject Name in English	Linear AlgebraI
Instructor	NAGAHARA MASAAKI
Instructor (Katakana)	ナガハラ　マサアキ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 1Term
Days, Periods, and Classrooms	(1T) Mon9-10,Fri9-10：IAS L102
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face, Online (simultaneous interactive), Online (on-demand)
Classes are primarily scheduled to be held in person. However, they may be switched to or combined with online (on-demand) sessions due to various circumstances. In such cases, the instructor will notify you through Momiji or other platforms.
Credits	2.0	Class Hours/Week	4	Language of Instruction	J : Japanese
Course Level	1 : Undergraduate Introductory
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Matrices, Determinants, Systems of Linear Equations, Vectors, Linear Spaces, Eigenvalues
Special Subject for Teacher Education		Special Subject
Class Status within Liberal Arts Education	This course serves as pre-specialized education with organic links to specialized studies. It aims to provide students with the foundational knowledge necessary for their respective fields, enabling them to master the logical framework and systems of basic disciplines, as well as the essential knowledge and skills for academic development.
Expected Outcome	The goal is for students to master the logical structure and systematic organization of the fundamental sciences in their respective subjects. By the end of the course, students will be able to articulate and explain the core knowledge and skills required for academic development.
Class Objectives /Class Outline	## Course Objectives In conjunction with "Linear Algebra II," this course aims to provide students with the fundamental knowledge and skills of linear algebra. ## Course Description This course covers approximately the first half of the following topics in linear algebra: - Matrix operations, regular matrices, and inverse matrices - Elementary matrix transformations, systems of linear equations, and matrix rank - Properties of determinants, determinant expansion, and Cramer's rule - Linear spaces, linear independence, and dimension - Linear maps, linear transformations, and orthogonal transformations - Eigenvalues, eigenvectors, and diagonalization
Class Schedule	[An Example of Class Schedule] lesson1: Matrix, Vector and Calculation of Matrices lesson2: Square Matrices and their Properties lesson3: Block Matrices lesson4: Simultaneous Linear Equations lesson5: Gaussian Elimination and Rank lesson6: Definition of Determinant lesson7: Solution of Simultaneous Linear Equations lesson8: Solution of Homogeneous Simultaneous Linear Equations lesson9: Introduction to Determinant lesson10: Permutations and their Properties lesson11: Sign of Permutation lesson12: Determinant and it basic Properties lesson13: Properties of Determinant lesson14: Laplace Expansion lesson15: Determinant of Special Types of Matrices Final Exam
Text/Reference Books,etc.	Gilbert Strang, Linear Algebra for Everyone, Wellesley-Cambridge Press, 2020. (Japanese translation: Strang: Kyoyo no Senkei Daisū, translated by Kiminori Matsuzaki and Kenji Hiranabe, Kindai Kagakusha, 2023.)
PC or AV used in Class,etc.	Text, moodle
(More Details)	Lecture slides will be distributed on Moodle after each class. Additionally, students are required to take review quizzes on Moodle to reinforce their understanding of the course content.
Learning techniques to be incorporated	Quizzes/ Quiz format
Suggestions on Preparation and Review	Please ensure that you purchase your own copy of the textbook and use it for both pre-class preparation and post-class review. To improve your skills, it is highly recommended that you solve the practice problems in the textbook for the sections covered in the lectures. While the solutions are in English, they are available at the following link: https://math.mit.edu/~gs/linearalgebra/ila5/ila5sols.pdf
Requirements
Grading Method	Please complete the review questions on Moodle after each lecture. Submission of these assignments will be used to record your attendance. Your final grade will be determined based on both attendance points and the results of the final examination.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	Each class includes a dedicated session for exercises. The goal is to establish a cycle of attending the lecture, working through problems independently, and verifying your results. By participating actively and keeping up with the coursework, you will have a solid grasp of fundamental linear algebra concepts by the time 1T concludes.
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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