Advanced Linear Algebra

Numbering Code U-LAS10 20006 LE55 Year/Term 2021 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year 2nd year students or above Target Student For science students
Language English Day/Period Fri.2
Instructor name Chang, Kai-Chun (Graduate School of Engineering Senior Lecturer)
Outline and Purpose of the Course Linear Algebra is an important tool commonly used in many fields, in not only mathematics but also natural sciences, engineering, etc. This course extends the contents in "Linear Algebra A/B" courses (provided majorly for 1st year students) and discusses advanced concepts of linear algebra, such as orthogonality, diagonalization, Singular Value Decomposition (SVD) of a matrix, Jordan canonical form, and their applications to real-world problems, etc.
Course Goals ・To acquire the advanced concepts of linear algebra, such as orthogonality, diagonalization, SVD of matrix.
・To understand the applications of linear algebra to real-world problems.
Schedule and Contents 1. Review of linear algebra [2 weeks]
- Big picture, rank, dimension, LU/LDU factorization, Gauss-Jordan elimination, etc.
- vector spaces, subspaces, nullspace, complete solutions, four subspaces and their dimensions and orthogonality, etc.

2. Orthogonality and its applications [3 weeks]
- Orthogonality and orthogonality complement, projections, least square approximations, orthogonal bases, Gram-Schumidt process, etc.

3. Eigenvalues, eigenvectors, and their applications [4 weeks]
- Eigenvalues and eigenvectors, diagonalization, matrix power, singular value decomposition (SVD) and their application to difference equations, differential equations and Markov process, etc.

4. Jordan canonical form [3 weeks]
- minimal polynomials, generalized eigenvectors, Jordan canonical form, and their applications.

5. Optional topics [2 weeks]
- numerical solutions, complex vectors and matrices, other applications, etc.

6. Feedback [1 week]
Evaluation Methods and Policy Quizzes or assignments (50%); final examination (50%)
Course Requirements Suggested prerequisites: Calculus A/B and Linear Algebra A/B or Calculus with Exercises A/B and Linear Algebra with Exercises A/B.
Study outside of Class (preparation and review) Students are expected to spend at least 2 hours per week on preview and review. More than half of that time is spent preparing for class and doing assignments.
References, etc. Introduction to Linear Algebra. 5th ed., Strang, G. (2009), (Wellesley-Cambridge Press)
Linear Algebra, 6th ed., Lipschutz, S. and Lipson, M. (2012), (McGraw-Hill)
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