## Advanced Linear AlgebraBack

Numbering Code | U-LAS10 20006 LE55 | Year/Term | 2021 ・ First semester |
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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. |
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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] |
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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) |