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.
Important notions are as follows:
vector space, linear span, linear map, isomorphism, commutative diagram, representation matrix, eigenvalue, eigenspace.
linear map, dual space, quotient space
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
Standard lecture course accompanied by discussion sessions
|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|
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.
Saito, Masahiko Introduction to Linear Algebra, University of Tokyo Press
To be evaluated based on exercises in discussion sessions and the final exam as a whole. Details will be announced during the course.
Students are expected to have passed Advanced Linear Algebra I