Course title
線形代数学Ⅱ   [Linear Algebra Ⅱ]
Course category	technology speciality courses	Requirement		Credit	2
Department		Year	1～4	Semester	3rd
Course type	3rd	Course code	021924
Instructor(s)
原 伸生   [HARA Nobuo]
Facility affiliation	Faculty of Engineering	Office	12-214	Email address

Course description

class code:　eclakaz 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 represetation. 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) to be able to calculate (bases of) the image and kernel of a linear map given by a matrix 3) to be able to calculate the representation matrix of a linear map with respect to given bases 4) to be able to calculate the eigen values and eigen spaces of a square matrix and determine whether it is diagonalizable 5) to be able to calculate an ortho-normalizion of a given basis of a metric space Corresponding criteria in the Diploma Policy: See the Curriculum maps

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. Summary: Exercise and/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 (metric space) 12. Gramm-Schmidt's ortho-normalization and orthogonal matrices 13. Orthonormal diagonalization of real symmetric matrices 14. Exercises summarizing the semester 15. Summary: Exercises and/or term examination

Prerequisites

Contents of "Linear Algebra I" in the spring semester. Remark: In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending appropriate amount of time and using the lecture handouts as well as the references specified below.

Required Text(s) and Materials

Miyake, T.: "Nyuumon-Senkei-Daisuu", Baifu-kan (in japanese) Remark: This lecture will be given in Japanese. Students who want to use a textbook written in English should consult the lecturer.

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

Arranged taking into account of students' requests

Remarks 1

Remarks 2

Related URL

Lecture Language

Japanese

Language Subject

Last update

9/12/2022 11:00:42 AM