2020 Advanced Linear Algebra II

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Academic unit or major
Undergraduate major in Mathematics
Mizumoto Shin-Ichiro 
Class Format
Lecture    (ZOOM)
Media-enhanced courses
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Offered quarter
Syllabus updated
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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.


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

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


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

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