### 2016　Linear Algebra II

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Academic unit or major
Basic science and technology courses
Instructor(s)
Brezina Jan
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(H113)  Thr1-2(H116)
Group
X
Course number
LAS.M106
Credits
2
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 focuses on basic principles of vector space and linear mapping, eigenvalue and diagonalization, inner produce of vector space.

The aim of this course is to understand 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

Besides lectures, a recitation class is opened every week in accordance with lectures.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Vector space, subspace Understand basics of vector spaces.
Class 2 Linear combination, linear independence, linear dependece Understand linear independence and related notions.
Class 3 Inner product and norm, Schwarz's inequality Understand the definition and properties of inner product and norm.
Class 4 Basis, dimension Understand basis and dimension of vector spaces.
Class 5 Existence of basis Understand a proof of the existence of a basis.
Class 6 Orthonormal basis, orthogonalization method of Schmitt Understand orthogonality and related notions.
Class 7 coordinate transformation, orthogonal matrix, unitary matrix Understand coordinate transformation and related notions.
Class 8 Linear transformation, kernel and image Understand linear transformation and related notions.
Class 9 Representation matrix of linear transformation Understand the representation matrix of linear transformation.
Class 10 Eigenvalue, eigenvector Understand the definition of an eigenvalue and an eigenvector.
Class 11 Characteristic polynomial, multiplicity, eigenspace Understand basics of vector spaces.
Class 12 Triangularization of matrices Understand the triangularization of matrices.
Class 13 Diagonalization of matrices Understand the diagonalization of matrices.
Class 14 Diagonalization of normal matrices, real symmetric matrix Understand notions related to diagonalization.
Class 15 Advanced topics Understand advanced topics of linear algebra.

### Textbook(s)

Linear Algebra in 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. Details will be announced during a lecture.

### Related courses

• LAS.M102 ： Linear Algebra I / Recitation
• LAS.M108 ： Linear Algebra Recitation II

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

Students are supposed to have completed Linear Algebra I / Recitation (LAS.M102).
Students must register Linear Algebra Recitation II (LAS.M108).

### Other

None in particular. 