### Linear Algebra II University of Tsukuba

#### Course Overview

Following “Linear Algebra I”’, “Linear Algebra II” will also concentrate on the basics of linear algebra. Emphasis will be given to topics that

will be useful in other disciplines, such as determinants, eigenvalues,

positive definite matrices, Fourier series and the Fast Fourier

Transform. Some homework problems may require you to use a program such as MATLAB or Mathematica, an important tool for numerical linear algebra.

No previous programming experience is required.

#### Learning Achievement

Following “Linear Algebra I”’, “Linear Algebra II” will also concentrate on the basics of linear algebra. Emphasis will be given to topics that will be useful in other disciplines, such as determinants, eigenvalues, positive definite matrices, Fourier series and the Fast Fourier Transform. Some homework problems may require you to use a program such as MATLAB or Mathematica, an important tool for numerical linear algebra. No previous programming experience is required.

#### Competence

Related to 1. Mathematical logic and calculation skills.

#### Course prerequisites

“Linear Algebra I” course

#### Grading Philosophy

Homework 40 %

Midterm Exam 30 %

Final Exam 30 %

#### Course schedule

Properties of determinants

Properties of determinants

Eigenvalues and eigenvectors

Eigenvalues and eigenvectors

Symmetric matrices and positive definite matrices

Symmetric matrices and positive definite matrices

Singular Value Decomposition (SVD)

Singular Value Decomposition (SVD)

Linear transformations and change of basis

Linear transformations and change of basis

Similar matrices and Jordan form

Similar matrices and Jordan form

Complex matrices and Fast Fourier transform

Complex matrices and Fast Fourier transform

Markov matrices and Fourier series

Markov matrices and Fourier series

Linear programming

Linear programming

#### Course type

Lectures and Class Exercises

#### Online Course Requirement

#### Instructor

Sharmin Sonia

#### Other information

The homework is essential in learning linear algebra. You are encouraged to talk to other students about difficult problems. But you must write your own solutions.

There will be a midterm one-hour exam at class times and a final exam. The use of calculators or notes is not permitted during the exams.

#### Site for Inquiry

Link to the syllabus provided by the university