Linear Algebra B

Time: Mon3 13:00-14:30

Class Room: Zoom Yoshida-South Campus Academic Center Bldg. North Wing 28

Lecturer: Atsushi Kanazawa (Kyoto University)

[Contact]

akanazawa(at mark)math.kyoto-u.ac.jp

Zoom office hour by appointment

[Description]

Linear algebra is one of the fundamental and important parts of mathematics. With Linear Algebra A and B, students are expected to understand not only the fundamental concepts of vector spaces and linear transformations, but also the concrete treatments of matrices and systems of linear equations. The objective of this course is to introduce linear algebra concepts such as vector spaces, linear transformations, matrices and systems of linear equations. In addition to learning linear algebra, students can learn how to discuss and present mathematical topics in English through this course.

[Lecture Note & Video]

Lecture Note (Comments are welcome!)

Lectures are recored and shared on PandA for reviews. 

[Reference]

The following is a standard linear algebra book (not really necessary for this lecture though). 

"Linear Algebra and Its Applications" by Jim Hefferon Free download

[Grade]

Lecture (online final exam) 70% + Exercise (7 reports) 30%

[Schedule]

10/5 1st Lecture: introduction, vector space, subspace

10/12 2nd Lecture: linear (in)dependence, basis, dimension

10/19 3rd Lecture: linear transformation, composition, kernel, image

10/26 4th Lecture: injection, surjection, isomorphism, dimension theorem

11/2 5th Lecture: dimension theorem, coordinate map, change of bases, matrix representation 

11/9 6th Lecture: matrix representation, change of matrix representations

11/16 7th Lecture: inner product, Cauchy–Schwarz inequality, orthonormal basis, projection

11/23 (勤労感謝の日, Labor Thanksgiving Day)

11/30 8th Lecture: Gram–Schmidt orthonormalization, orthogonal transformation, Hermitian inner product

12/7 9th Lecture: unitary transformation, orthogonal complement, eigenvalue problem

12/14 10th Lecture: eigenvalue, eigenvector, eigenspace, characteristic polynomial

12/21 11th Lecture: diagonalization, application (power, square, sequence etc)

12/28 12th Lecture: application, diagonalization of Hermitian (symmetric) matrix

1/11 (成人の日, Coming of Age Day)

1/18 13th Lecture: Review Session

1/25 14th Lecture: Online Final Exam (open-book style)