### 2020　Linear Algebra II P(31～40)

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Basic science and technology courses
Instructor(s)
Nosaka Takefumi
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Tue3-4(W541)  Thr1-2(W541)
Group
P(31～40)
Course number
LAS.M106
Credits
2
2020
Offered quarter
3Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

Building on the content of "Linear Algebra I", the instructor will explain the fundamentals of vector spaces and linear mapping, eigenvalues and diagonalization, and the inner product of vector spaces.

The aim of this course is to explain the theory of vector spaces which will be important for science and engineering.

### Student learning outcomes

This course follows "Linear Algebra I: Exercise". Students will acquire the fundamentals of linear algebra. They will also deepen and further develop their understanding of content learned in "Linear Algebra I".

### 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

Aside from the lecture, exercises will be done once a week in tune with the progress of the lecture.

### 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 dependence Understand linear independence and related notions.
Class 3 Basis, dimension Understand basis and dimension of vector spaces.
Class 4 Existence of basis Understand a proof of the existence of a basis.
Class 5 Linear transformation, kernel and image Understand linear transformation and related notions.
Class 6 Representation matrix of linear transformation Understand the representation matrix of linear transformation.
Class 7 Inner product and norm, Schwarz's inequality Understand the definition and properties of inner product and norm.
Class 8 Orthonormal basis, orthogonalization method of Schmitt Understand orthogonality and related notions.
Class 9 Coordinate transformation, orthogonal matrix, unitary matrix Understand coordinate transformation and related notions.
Class 10 Eigenvalue, eigenvector Understand the definition of an eigenvalue and an eigenvector.
Class 11 Characteristic polynomial, multiplicity, eigenspace Understand the properties of eigenvalues.
Class 12 Triangularization and diagonalization of matrices Understand the triangularization and diagonalization of matrices.
Class 13 Diagonalization of normal matrices, diagonalization real symmetric matrix Understand notions related to diagonalization.

### 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)

Miyake "Introduction to Linear Algebra, Miyake”, Baifukan

TBA

### Assessment criteria and methods

Based on overall evaluation on the results of quizzes, reports, mid-term and final examinations. Details will be announced in class.

### 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).

### Other

None in particular.