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)
柴田 和樹   [SHIBATA Kazuki]
Facility affiliation	Graduate School of Engineering	Office		Email address

Course description

Linear algebra is the base on various field. In this course, we will learn basic properties of vector spaces and we will also learn about eigenvalues and eigenvectors, for deep understanding of linear algebra.

Expected Learning

The goals of this course are (1) to compute bases and dimensions of vector spaces, (2) to be capable of performing their practical calculations.

Course schedule

1. Vector spaces and their subspaces 2. Linear independence and linear dependence 3. Maximum of linearly independent vectors 4. Bases and dimensions of vector spaces 5. Definition of linear maps and the kernel and the image of linear maps 6. Representation matrices of linear maps 7. Midterm examination 8. Eigenvalues and eigenvectors 9. Diagonalization of square matrices 10. Inner product spaces: inner product of real vectors, orthogonal sets and orthogonal matrices 11. Orthonormal bases: Gram-Schmidt orthonormalization 12. Diagonalization of real symmetric matrices 13. Cayley-Hamilton theorem 14. Exercises 15. Term examination

Prerequisites

Knowledge of the course of Linear Algebra Ⅰ will be used in the lecture.

Required Text(s) and Materials

References

Assessment/Grading

Midterm exam. (50%), Term exam. (50%)

Message from instructor(s)

Linear algebra Ⅱ is the abstract concept. For deep understanding, solve exercises.

Course keywords

Vector space, Basis, Dimension, Linear map, Representation matrix, Eigenvalues and eigenvectors, Diagonalization

Office hours

Remarks 1

Remarks 2

Related URL

Lecture Language

Language Subject

Last update

9/18/2018 11:49:31 AM