Hiroshima University Syllabus

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Academic Year 2023Year School/Graduate School Liberal Arts Education Program
Lecture Code 63071002 Subject Classification Foundation Courses
Subject Name 線形代数学II[1理数]
Subject Name
Subject Name in
Linear AlgebraII
キムラ シュンイチ
Campus Higashi-Hiroshima Semester/Term 1st-Year,  Second Semester,  3Term
Days, Periods, and Classrooms (3T) Weds3-4,Fri5-6:IAS K109
Lesson Style Lecture Lesson Style
(More Details)
Lectures, Blackboard 
Credits 2.0 Class Hours/Week   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 First Year Students
Keywords Vectors, Matrices, Determinants, Cofactor Matrices, Abstract Linear Algebra, Basis, Sub Linear Space, Dual Space, Eigenvalue, Eigenvector, Diagonalization, Upper Triangular Matrix, Cayley-Hamilton theorem, Constant coefficient ordinary differential equation 
Special Subject for Teacher Education   Special Subject  
Class Status within
Liberal Arts Education
As pre-specialized education, which is organically linked to specialized education, Foundation Courses are aimed at providing students with the basic knowledge necessary to understand specialized studies in their chosen areas, and thereby providing them w 
Expected OutcomeTo understand, acquire, and be able to explain the logical structure and system of the basic disciplines in accordance with each subject and the knowledge and skills necessary for further academic development. 
Class Objectives
/Class Outline
One can define additions and scalar multiplications for geometric vectors, without reference to the coordinates.  A set V is called Abstract Linear Space when addition and scalar multiplication are defined, and identified with the number linear space once a basis (therefore a coordinate) is fixed.  We learn how to treat Abstract Linear Space.  Also we learn how to compute Eigenvalues, Eigenvectors and how to use them. 
Class Schedule lesson1 Review: Gauss Elimination and Determinant
lesson2 Calculation of Determinants
lesson3 Determinants of various matrices
lesson4 Abstract Linear Space
lesson5 Axioms
lesson6 Basis
lesson7 Sublinear Spaces
lesson8  Image and Kernel
lesson9 Midterm
lesson10 Eigenvalues and Eigenvectors
lesson11 Diagonalization
lesson12 Applications of eivenvectors (1)
lesson13 Applications of eivenvectors (2)
lesson14 Cayley-Hamilton Theorem
lesson15 Final Exam

Midterm and Final Exam.  Also some reports 
Senkeidaisuugakunyumon (Tokyo Tosho) Shun-ichi Kimura 
PC or AV used in
(More Details) Textbook 
Learning techniques to be incorporated  
Suggestions on
Preparation and
Review every lecture carefully.  Students are supposed to understand the previous lectures.   
Requirements Based on the lecture of Linear AlgebraI 
Grading Method The grade will be based on final examination, midterm examination, and/or assignments. 
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
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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