Course title
線形代数学Ⅱ   [Linear Algebra Ⅱ]
Course category	technology speciality courses	Requirement		Credit	2
Department	Department of Biotechnology and Life Science, Biotechnology and Life Science(~2018)	Year	1～4	Semester	3rd
Course type	3rd	Course code	021917
Instructor(s)
直井 克之   [NAOI Katsuyuki]
Facility affiliation	Faculty of Engineering	Office	building 12, room 226	Email address

Course description

Linear algebra provides indispensable tools to analyze various mathematical phenomena appearing in engineering. 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 eigenvalues and eigenspaces, 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 Corresponding criteria in the Diploma Policy: See the Curriculum maps.

Course schedule

1. Vector spaces and their subspaces 2. Linear independence 3. Maximum number of linearly independent vectors 4. Bases and the dimension of a vector space 5. Linear maps: their images and kernels 6. Computations involving linear maps 7. Exercise 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. Exercise Term examination

Prerequisites

Contents of "Linear Algebra I" in the spring semester In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the University.

Required Text(s) and Materials

入門線形代数（三宅敏恒）培風館

References

線形代数演習（斎藤正彦）東京大学出版会

Assessment/Grading

Midterm exam (40%), Term exam (40%), class performance (20%)

Message from instructor(s)

Course keywords

vector space, linear map, linear independence, basis, dimension, representation matrix, eigenvalue, eigenspace, diagonalization, inner product

Office hours

after the class

Remarks 1

Remarks 2

Related URL

Lecture Language

Japanese

Language Subject

Last update

4/1/2019 11:31:26 AM