### 2016　Linear Algebra Recitation II

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Academic unit or major
Basic science and technology courses
Instructor(s)
Brezina Jan
Class Format
Exercise
Media-enhanced courses
Day/Period(Room No.)
Wed1-2(H116)
Group
X
Course number
LAS.M108
Credits
1
2016
Offered quarter
3Q
Syllabus updated
2016/4/27
Lecture notes updated
-
Language used
English
Access Index ### Course description and aims

Based on "Linear Algebra I", this course discusses the basics of vector space and linear mapping, eigenvalue and diagonalization, inner produce of vector space.

The aim of this recitation course is to cultivate better understanding about the theory of vector spaces which is important in learning science and engineering.

### Student learning outcomes

Following "Linear algebra I", this course gives the foundation of linear algebra. This course aims for deeper understanding and development of knowledge on the theory of Linear Algebra.

### Keywords

Vector space, basis, linear transformation, eigenvalue, diagonalization

### Competencies that will be developed

 Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

A recitation class is opened every week in accordance with lectures.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Vector space, subspace Help better understand the notions of vector space.
Class 2 Linear combination, linear independence, linear dependence,inner product and norm, Schwarz's inequality Help better understand the notion of linear independence.
Class 3 Basis, dimension, existence of basis Help better understand the notion of basis.
Class 4 Orthonormal basis, orthogonalization method of Schmitt,coordinate transformation, orthogonal matrix, unitary matrix Help better understand orthonormal basis and related notion.
Class 5 Linear transformation, kernel and image, basis, dimension, representation matrix of linear transformation Help better understand linear transformation and related notions.
Class 6 Eigenvalue, eigenvector, characteristic polynomial, multiplicity, eigenspace Help better understand eigenvalue problems.
Class 7 Triangularization of matrices, diagonalization of matrices Help better understand diagonalization and related notions.
Class 8 Diagonalization of normal matrices, real symmetric matrix, advanced topics Help better understand real symmetric matrices and related notions.

### Textbook(s)

Linear Algebra by English, Catherine Oikonomides, Eiji Yanagida

### Reference books, course materials, etc.

None in particular

### Assessment criteria and methods

Based on overall evaluation of the results for quizzes, report, mid-term and final examinations.

### Related courses

• LAS.M102 ： Linear Algebra I / Recitation
• LAS.M106 ： Linear Algebra II

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are supposed to have completed Linear Algebra I / Recitation (LAS.M102).
Students are required to complete Linear Algebra II (LAS.M106).

### Other

None in particular 