Course title
線形代数学Ⅱ   [Linear Algebra Ⅱ]
Course category	technology speciality courses,ets.	Requirement		Credit	2
Department		Year	1～4	Semester	Fall
Course type	Fall	Course code	021519
Instructor(s)
原 伸生   [HARA Nobuo]
Facility affiliation	Faculty of Engineering	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

10/6/2017 10:49:06 AM