Course title
線形代数学Ⅱ   [Linear Algebra Ⅱ]
Course category technology speciality courses  Requirement   Credit 2 
Department   Year 14  Semester 3rd 
Course type 3rd  Course code 021917
Instructor(s)
柴田 和樹   [SHIBATA Kazuki]
Facility affiliation Graduate School of Engineering Office afjgxte/L1151  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.

Kazuki Shibata (a part-time lecturer) will be in charge of this course.
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.

Corresponding criteria in the Diploma Policy: See the Curriculum maps
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. Review, and 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. Review, and Term examination
Prerequisites
Knowledge of the course of Linear Algebra Ⅰ will be used in the lecture.
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 and using the lecture handouts as well as the references specified below.
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
It will be announced in the first lecture.
Remarks 1
Classcode of Google Classroom is q263xvq.
Remarks 2
Related URL
Lecture Language
Japanese
Language Subject
Last update
9/24/2021 12:42:02 AM