Linear Algebra

Course Information

College	Tsuyama College	Year	2021
Course Title	Linear Algebra
Course Code	0014	Course Category	Specialized / Elective
Class Format	Lecture	Credits	Academic Credit: 2
Department	Advanced Mechanical and Control System Engineering Course	Student Grade	Adv. 1st
Term	First Semester	Classes per Week	2
Textbook and/or Teaching Materials
Instructor	MATSUDA Osamu

Course Objectives

In this course, you will learn the theory of n-dimensional number vector space. In particular, learn new concepts such as Jordan normal form, quaternions, and groups.
Acquire the basic idea of ​​the theory of n-dimensional number vector space.
1. 1. Understand n-dimensional number vector space.
2. Understand the concept of inner product and distance.
3. Geometrically explain the difference in space deformation depending on the type of matrix.
4. Explain the representation matrix and the change of basis.
5. Understand the concept of Jordan normal form.
6. Understand quaternions and the rotation of space.

Rubric

	Excellent	Good	Acceptable	Not acceptable
Achievement 1	A good understanding of n-dimensional number vector spaces.	Understand about 70% of the n-dimensional number vector space.	Understand about 60% of the n-dimensional number vector space.	Don't understand the n-dimensional number vector space.
Achievement 2	A good understanding of inner product and distance.	About 70% have an understanding of inner product and distance.	About 60% have an understanding of inner product and distance.	Don't understand the inner product and distance.
Achievement 3	It is possible to explain the difference in the deformation of space depending on the type of matrix geometrically and precisely.	Geometrically, about 70% of the differences in spatial deformation depending on the type of matrix can be explained.	Geometrically, about 60% of the differences in spatial deformation depending on the type of matrix can be explained.	It is not possible to geometrically explain the difference in the deformation of space depending on the type of matrix.
Achievement 4	Explain the representation matrix and the basis basis precisely.	Explain about 70% of representation matrices and basis transformations.	Explain about 60% of representation matrices and basis transformations.	Can't explain the representation matrix and the change of basis.
Achievement 5	The idea of ​​Jordan normal form is well understood.	About 70% of the Jordan normal form is known.	About 60% of the Jordan normal form is known.	Don't understand the idea of ​​Jordan normal form.
Achievement 6	A good understanding of quaternions and the rotation of space.	Understand about 70% of quaternions and the rotation of space.	Understand about 60% of quaternions and the rotation of space.	Don't understand the quaternion and the rotation of space.

Teaching Method

Outline:

General or Specialized : Specialized

Field of learning : Natural science Common / Basic

Required, Elective: Elective must complete subjects

Foundational academic disciplines : Mathematical science / Mathematics / Analysis basics

Relationship with Educational Objectives : This subject corresponds to the learning goal "(2) Acquire basic science and technical knowledge".

Relationship with JABEE programs : The main goal of learning / education in this class are "(A) , A-1".

Class Outline: In Applied Mathematics I, you will learn the basics of probability theory and statistics. In probability theory, we look at the theory of distributions (binomial distribution, Poisson distribution, normal distribution) and the central limit theorem, which are important in statistical processing. Learn the equations of correlation and regression line as an arrangement of two-variable data. Finally, learn how to estimate and test the population.

Style:

Course method : Focus on understanding the content on the board, and assign as many exercises as possible to deepen understanding.

Grade evaluation method : 4 regular exams (50%) and other exams, exercises, reports and effort of class(50%). etc, A re-examination may be conducted. The retest will be evaluated in the same way as the main test, with an upper limit of 80 points. Textbooks, notebooks, etc. are not allowed for the exam.

Notice:

Precautions on enrollment : Students must take this class (no more than one-third of the required number of class hours missed) in order to complete the academic year.

Course advice: This course teaches the basic ideas of ​​probability and statistical methods required for engineering, so this course is of great importance.


Foundational subjects : Fundamental Mathematics (1st year), Fundamental Linear Algebra (2nd), Differential and Integral Ⅰ(2nd), Differential and Integral Ⅱ (3rd), Differential Equations (3rd)

Related subjects: Mathematics, physics, and other subjects after the third year

Attendance advice : If you are late after, you may be treated as absent after a warning.

Characteristics of Class / Division in Learning

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Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Guidance
		2nd	n-dimensional space number vector space	Understanding the definition of n-dimensional space number vector space
		3rd	Dot product and Gram-Schmidt orthogonalization method	Understanding the definition of inner product and understanding Gram-Schmidt's orthogonalization method
		4th	Transformation of space by matrix Part 1	Understanding the deformation of space by a matrix Part 1
		5th	Transformation of space by matrix Part 2	Understanding the deformation of space by a matrix Part 2
		6th	Relationship between representation matrix and coordinates	Understanding the relationship between the representation matrix and coordinates
		7th	Dimension theorem	Understanding the dimensional theorem
		8th	Mid-term exam	Confirm basic matters
	2nd Quarter
		9th	Jordan normal form part 1	Understanding Jordan Normal Form Part 1
		10th	Jordan normal form part 2	Understanding Jordan Normal Form Part 2
		11th	Jordan decomposition 1 part 1	Understanding of Jordan Decomposition 1 Part 1
		12th	Jordan decomposition 1 part 2	Understanding of Jordan Decomposition 1 Part 2
		13th	Complex numbers and quaternions	Understanding complex numbers and quaternions
		14th	Quaternion and rotation	Understanding quaternions and rotations
		15th	Last term exam	Confirm basic matters
		16th	Return of answer and explanation of answer

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Other	Total
Subtotal	50	0	0	50	0	0	100
Basic Proficiency	50	0	0	50	0	0	100
Specialized Proficiency	0	0	0	0	0	0	0
Cross Area Proficiency	0	0	0	0	0	0	0