Course title
線形代数学Ⅱ   [Linear Algebra Ⅱ]
Course category technology speciality courses,ets.  Requirement   Credit 2 
Department   Year 14  Semester Fall 
Course type Fall  Course code 021210
Instructor(s)
澤田 伸晴   [SAWADA Nobuharu]
Facility affiliation Graduate School of Engineering Office   Email address

Course description
In this course, the notion of a vector space and a linear map between two vector spaces will be introduced. We will learn various basic properties of a basis and the dimension of a vector space, and the image and the kernel of a linear map. We will also learn about an eigenvalue and an eigenvector, for deep understanding of linear algebra.
Expected Learning
The goals of this course are
(1) to understand vector spaces, linear maps, eigenvalues, eigenvectors, inner products and diagonalization, and
(2) to be capable of performing their practical calculations.
Course schedule
1. Vector spaces
2. Vector spaces and their subspaces
3. Linear independence and linear dependence
4. Maximum of linearly independent vectors
5. Bases and dimensions of vector spaces
6. Linear maps
7. Representation matrices of linear maps
8. Exercises, or midterm examination
9. Eigenvalues and eigenvectors
10. Diagonalization of square matrices
11. Inner products and complex numbers
12. Orthonormalization and orthogonal matrices
13. Diagonalization of real symmetric matrices
14. Cayley-Hamilton theorem
15. Term examination
Prerequisites
Knowledge of the course of Linear Algebra I will be used in the lecture.
Required Text(s) and Materials
References
MIYAKE, Toshitsune, “Nyuumon-Senkei-Daisuu”, Baifu-kan (in Jananese),
SAITO, Masahiko, “Senkei-Daisuu-Nyuumon”, Tokyo Daigaku shuppan-kai (in Japanese),
SATAKE, Ichiro, “Senkei-Daisuugaku”, Shoukabou (in Japanese).
Assessment/Grading
Exercises or Midterm exam (50%), Term exam (50%)
Message from instructor(s)
Course keywords
vector space, linear map, linear independence, basis, dimension, eigenvalue, eigenspace, diagonalization
Office hours
Remarks 1
Remarks 2
Related URL
Lecture Language
Language Subject
Last update
9/29/2017 8:38:40 AM