Course title
401034001
Linear Algebra 2
 HIROSE Sampei SATO Takamichi NAKAGAWA Takahiro
Course description
Linear algebra is an algebraic and geometric theory of properties called linearity. In Linear Algebra 1, we focused on algebraic properties and learned about them.
In this class, students learn about linear algebra from a geometric standpoint, including vector spaces and linear mappings.
Purpose of class
The purpose of this class is to understand the geometric meaning of the content learned in Linear Algebra 1 and to be able to calculate it.
Goals and objectives
1. To be able to verify the basic properties of numerical vector spaces with concrete examples.
2. To be able to verify the basic properties of vector spaces with concrete examples.
3. To be able to verify the basic properties of linear mappings with concrete examples.
4. To be able to verify the basic properties of metric vector spaces with concrete examples.
5. To be able to verify the geometric meaning of linear and affine transformations with concrete examples.
Language
Japanese
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Numerical vector space, inner product and outer product Read through the textbook p.83-p.93 and handouts, and solve the exercises before class. Review after class. 190minutes
2. Line, plane and quadratic curve Read through the textbook p.93-p.101 and handouts, and solve the exercises before class. Review after class. 190minutes
3. Vector space and linear independence Read through the textbook p.103-p.117 and handouts, and solve the exercises before class. Review after class. 190minutes
4. Basis and dimension Read through the textbook p.117-p.126 and handouts, and solve the exercises before class. Review after class. 190minutes
5. Linear mapping and linear isomorphism Read through the textbook p.129-p.136 and handouts, and solve the exercises before class. Review after class. 190minutes
6. Matrix representation of linear mapping, composite mapping and inverse mapping Read through the textbook p.137-p.148 and handouts, and solve the exercises before class. Review after class. 190minutes
7. Midterm examination and its explanation Preparation of midterm examination. 190minutes
8. Inner product and orthonormal basis Read through the textbook p.171-p.179 and handouts, and solve the exercises before class. Review after class. 190minutes
9. Orthogonal transformation and diagonalization of symmetric matrix Read through the textbook p.179-p.187 and handouts, and solve the exercises before class. Review after class. 190minutes
10. Quadratic form Read through the textbook p188-p.193 and handouts, and solve the exercises before class. Review after class. 190minutes
11. Geometric meaning of linear transformations 1 Read through the textbook p.197-p.205 and handouts, and solve the exercises before class. Review after class. 190minutes
12. Geometric meaning of linear transformations 2 Read through the textbook p.205-p.210 and handouts, and solve the exercises before class. Review after class. 190minutes
13. Affine transformation and its geometric meaning Read through the textbook p.148-p.153, p.211-p.212 and handouts, and solve the exercises before class. Review after class. 190minutes
14. Final examination and its explanation Preparation of final examination. 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Midterm examination Final examination Reports and little examinations Total.
1. 10% 7% 17%
2. 10% 7% 17%
3. 10% 6% 16%
4. 15% 10% 25%
5. 15% 10% 25%
Total. 30% 30% 40% -
Evaluation method and criteria
Midterm examination(30%), Final examination(30%), Reports and little examinations(40%)
60% if students can understand and solve exercises in the handouts
Textbooks and reference materials
Textbook: 工学系のための線形代数、黒川康宏、佐々木真二、廣瀬三平、山澤浩司、東京図書
Prerequisites
Review Linear Algebra 1
Office hours and How to contact professors for questions
• 30 minutes after class
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
• Course that cultivates an ability for utilizing knowledge
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A 該当しない
Education related SDGs:the Sustainable Development Goals
• 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE