### 2023　Linear Algebra Recitation II Q(41～50)

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Academic unit or major
Basic science and technology courses
Instructor(s)
Kawai Shingo
Class Format
Exercise    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Wed1-2(M-178(H1101))
Group
Q(41～50)
Course number
LAS.M108
Credits
1
2023
Offered quarter
4Q
Syllabus updated
2023/3/20
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

Based on "Linear Algebra I", this course discusses basic part of vector space and linear mapping, eigenvalue and diagonalization, and inner product of vector space.

The aim of this recitation is to cultivate a better understanding of the theory of vector spaces which will be important for
science and engineering.

### Student learning outcomes

Following "Linear algebra I", this course is concerned with the foundation of linear algebra. This course aims for a deeper understanding and development of 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 held every week in accordance with the progress of the lectures. Details will be announced in class.

### 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 Help better understand the notion of linear independence.
Class 3 Basis, dimension, existence of basis Help better understand the notion of basis.
Class 4 Linear transformation, kernel and image, representation matrix of linear transformation Help better understand linear transformation and related notions.
Class 5 Orthonormal basis, inner product and norm, Schwarz's inequality, orthogonalization method of Schmitt Help better understand orthonormal basis and related notion.
Class 6 Eigenvalue, eigenvector, characteristic polynomial, multiplicity, eigenspace, triangularization and diagonalization of matrices Help better understand eigenvalue problems.
Class 7 Diagonalization of normal matrices, diagonalization of real symmetric matrix Help better understand diagonalization and related notions.

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

### Textbook(s)

See the syllabus of Linear Algebra II (LAS.M106).

### Reference books, course materials, etc.

See the syllabus of Linear Algebra II (LAS.M106).

### Assessment criteria and methods

Based on overall evaluation on the results of quizzes, reports, 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 recommended to take Linear Algebra II (LAS.M106) at the same time.

### Other

None in particular.