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 021411
Instructor(s)
奥田 喬之   [OKUDA Takayuki]
Facility affiliation Graduate School of Agriculture Office 12-214  Email address

Course description
In this course we introduce the notion of an abstract vector space as a generalization of the space of plane or space vectors, as well as a linear map between two vector spaces, which is studied with its matrix representation. In particular, we will learn about basic properties and computation of a basis and the dimension of a vector space, the image and kernel of a linear map. We also learn about the concepts and methods of eigen values and eigen spaces, diagonalization, and metric spaces, aiming at better understanding of linear algebra.
Expected Learning
The goal of this course is:
1) to understand basic notions of vector spaces, linear maps, linear independence and bases
2) capable to calculate (bases of) the image and kernel of a linear map given by a matrix
3) capable to calculate the representation matrix of a linear map with respect to given bases
4) capable to calculate the eigen values and eigen spaces of a square matrix and determine whether it is diagonalizable
5) capable to ortho-normalize a given basis of a metric space
Course schedule
1. Review of spring semester
2. Vector spaces and their subspaces
3. Linear independence
4. Bases and the dimension of a vector space
5. Linear maps: their images and kernels
6. Computations involving linear maps
7. Exercise,or midterm examination
8. Representation matrices of linear maps
9. Eigenvalues, eigenvectors and eigenspaces
10. Diagonalization of square matrices
11. Vector spaces with inner product (real/complex Hermitian)
12. Schmidt's Orthonormalization and orthogonal matrices
13. Orthonormal diagonalization of real symmetric matrices
14. Exercises summarizing the semester
15. Term examination
Prerequisites
Contents of "Linear Algebra I" in the spring semester
Required Text(s) and Materials
Miyake, T.: "Nyuumon-Senkei-Daisuu", Baifu-kan (in japanese)
References
To be indicated in the lecture
Assessment/Grading
Midterm exam (50%), Term exam (50%)
Message from instructor(s)
Course keywords
vector space, linear map, linear independence, basis, dimension, representation matrix, eigenvalue, eigenspace, diagonalization, inner product
Office hours
Remarks 1
Remarks 2
Related URL
Lecture Language
Japanese
Language Subject
Last update
3/9/2017 2:40:27 PM