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- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Basic science and technology courses
- Instructor(s)
- Minagawa Tatsuhiro
- Class Format
- Exercise
- Media-enhanced courses
- Day/Period(Room No.)
- Wed1-2(W521)
- Group
- O(21〜30)
- Course number
- LAS.M108
- Credits
- 1
- Academic year
- 2016
- Offered quarter
- 3Q
- Syllabus updated
- 2017/1/11
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
Based on "Linear Algebra I", this course discusses basic part of vector space and linear mapping, eigenvalue and diagonalization, and inner product of vector space.
The aim of this recitation is to cultivate a better understanding of the theory of vector spaces which will be important for
science and engineering.
Student learning outcomes
Following "Linear algebra I", this course is concerned with the foundation of linear algebra. This course aims for a deeper understanding and development of the theory of Linear Algebra.
Keywords
Vector space, basis, linear transformation, eigenvalue, diagonalization
Competencies that will be developed
| Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
A recitation class is held every week in accordance with the progress of the lectures.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Vector space, subspace | Help better understand the notions of vector space. |
| Class 2 | Linear combination, linear independence, linear dependence,inner product and norm, Schwarz's inequality | Help better understand the notion of linear independence. |
| Class 3 | Basis, dimension, existence of basis | Help better understand the notion of basis. |
| Class 4 | Orthonormal basis, orthogonalization method of Schmitt,coordinate transformation, orthogonal matrix, unitary matrix | Help better understand orthonormal basis and related notion. |
| Class 5 | Linear transformation, kernel and image, basis, dimension, representation matrix of linear transformation | Help better understand linear transformation and related notions. |
| Class 6 | Eigenvalue, eigenvector, characteristic polynomial, multiplicity, eigenspace | Help better understand eigenvalue problems. |
| Class 7 | Triangularization of matrices, diagonalization of matrices | Help better understand diagonalization and related notions. |
| Class 8 | Diagonalization of normal matrices, real symmetric matrix, advanced topics | Help better understand real symmetric matrices and related notions. |
Textbook(s)
Takeshi Kajiwara, Introduction to linear spaces, Nihon Hyoronsha
Reference books, course materials, etc.
Takeshi Kajiwara, Lectures on linear algebra, Nihon Hyoronsha
Takeshi Kajiwara, The secret to linear algebra, Kyoritsu shuppan
Assessment criteria and methods
Based on overall evaluation of the results for quizzes, report, mid-term and final examinations.
Related courses
- LAS.M102 ： Linear Algebra I / Recitation
- LAS.M106 ： Linear Algebra II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are supposed to have completed Linear Algebra I / Recitation (LAS.M102).
Students are required to register Linear Algebra II (LAS.M106).
Other
None in particular.
