### 2019　Advanced Linear Algebra II

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Instructor(s)
Mizumoto Shin-Ichiro
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Wed3-4(H135)
Group
-
Course number
MTH.A212
Credits
1
2019
Offered quarter
2Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

Students in this course will study the concept and examples of vector space in linear algebra. Exercise problems will be presented in class to cement understanding. This course follows "Advanced Linear Algebra I. "

Prior experience with linear algebra using specific matrices is assumed, and this course discusses in detail from the basics of vector space to linear mapping to eigenvalues and the like. These activities are important, also serving as practical exercises for students to acquire basic methods in learning other fields of advanced mathematics.

### Student learning outcomes

Important notions are as follows:
vector space, linear span, linear map, isomorphism, commutative diagram, representation matrix, eigenvalue, eigenspace.

### Keywords

linear map, dual space, quotient space

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

Standard lecture course accompanied by discussion sessions

### Course schedule/Required learning

Course schedule Required learning
Class 1 Isomorphism and applications Details will be provided during each class session
Class 2 representation matrix Details will be provided during each class session
Class 3 change of basis and commutative diagram Details will be provided during each class session
Class 4 eigenvalue and eigenspace Details will be provided during each class session
Class 5 invariant subspace Details will be provided during each class session
Class 6 application of diagonalization Details will be provided during each class session
Class 7 quotient space, dual space Details will be provided during each class session
Class 8 evaluation of progress Details will be provided during each class session

None required

### Reference books, course materials, etc.

Saito, Masahiko Introduction to Linear Algebra, University of Tokyo Press

### Assessment criteria and methods

To be evaluated based on exercises in discussion sessions and the final exam as a whole. Details will be announced during the course.

### Related courses

• MTH.A211 ： Advanced Linear Algebra I

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are expected to have passed Advanced Linear Algebra I