Linear Algebra

Course title

M2017000

Linear Algebra

Course description

We conduct in-person (face-to-face) classes in Spring 2023. Those who are based abroad and wish to take the classes online should contact the lecturer via email (ikegami@shibaura-it.ac.jp).

In this course, you will learn the basic theory of matrices and their algebras with applications to linear equations and differential equations. Starting with how to represent linear equations via matrices, you will study the row and column operations of matrices with its application to solving linear equations with Gaussian elimination. Looking at solution sets of linear systems, you will reach the notions of linear independence of vectors, linear transformations, and vector spaces. Then you will learn the rank, determinant, eigenvalues, and eigenvectors of matrices to characterize the basic properties of matrices and linear equations. You will also see the correspondence between matrices and linear transformations of vector spaces.

Purpose of class

You are expected to obtain skills, knowledge, and understandings of basics of matrices and linear transformations, which are widely used in science and engineering.

Goals and objectives

	Goals and objectives	Course Outcomes
1.	The students can use basic operations of matrices to solve a linear equation with Gaussian elimination.	A-1
2.	The students can raise concrete & non-trivial examples of the four fundamental vector subspaces and for each such example, they can find a basis and determine its dimension.	A-1
3.	The students can use Gram-Schmidt to find an orthonormal basis for a given subspace of a vector space.	A-1
4.	The students can use eigenvariables & eigenvectors of a given matrix A to diagonalize A and to compute the power of A.	A-1
5.	The students can raise concrete examples of a linear transformation and can determine whether a given transformation is linear or not.	A-1

Language

English

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Introduction to Linear Algebra The geometry of linear equations Elimination with matrices	Review the content of the lecture (1.1-1.3, 2.1-2.3 in the textbook)	200分
1.		Preparation for Quiz	180分
2.	Matrix operations and inverses Elimination and factorization	Review the content of the lecture (2.4-2.6 in the textbook)	160分
2.		Preparation for Quiz	220分
3.	Transposes Vector spaces and subspaces	Review the content of the lecture (2.7, 3.1 in the textbook)	120分
3.	Transposes Vector spaces and subspaces	Preparation for Quiz	260分
4.	The nullspace The complete solution to Ax = b	Review the content of the lecture (3.2-3.3 in the textbook)	160分
4.	The nullspace The complete solution to Ax = b	Preparation for Quiz	220分
5.	Basis and dimension The four fundamental subspaces	Review the content of the lecture (3.4-3.5 in the textbook)	160分
5.	Basis and dimension The four fundamental subspaces	Preparation for Quiz	220分
6.	Orthogonality Projections and subspaces	Review the content of the lecture (4.1-4.2 in the textbook)	120分
6.	Orthogonality Projections and subspaces	Preparation for the mid-term exam	240分
7.	Mid-term exam and discussions on the solutions afterwards	Preparation for & Review of the mid-term exam	380分
8.	Least squares approximations Orthonormal bases and Gram-Schmidt	Review the content of the lecture (4.3-4.4 in the textbook)	140分
8.		Preparation for Quiz	240分
9.	Properties of determinants Formulas for determinants	Review the content of the lecture (5.1-5.2 in the textbook)	160分
9.	Properties of determinants Formulas for determinants	Preparation for Quiz	220分
10.	Applications of determinants Eigenvalues and eigenvectors	Review the content of the lecture (5.3, 6.1 in the textbook)	160分
10.	Applications of determinants Eigenvalues and eigenvectors	Preparation for Quiz	220分
11.	Diagonalization	Review the content of the lecture (6.2 in the textbook)	160分
11.	Diagonalization	Preparation for Quiz	220分
12.	Linear transformations The Matrix of a Linear Transformation	Review the content of the lecture (8.1, 8.2 in the textbook)	160分
12.		Preparation for Quiz	220分
13.	Reviews	Work on exercises	160分
13.	Reviews	Preparation for the final exam	220分
14.	Final exam and discussions on the solutions afterwards	Preparation for & Review of the final exam	380分
Total.	-	-	5300分

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Quiz and Mid-term exam	Final exam	Total.
1.	15%	10%	25%
2.	15%	10%	25%
3.	10%	10%	20%
4.	10%	10%	20%
5.	0%	10%	10%
Total.	50%	50%	-

Evaluation method and criteria

Quiz and mid-term exam will contribute 50% of your grade.
Final exam will contribute 50% of your grade.
Those who get at least 60% of the full score will pass this course.

Feedback on exams, assignments, etc.

ways of feedback	specific contents about "Other"
The Others	The lecturer will give feedback both in class and through the google classroom.

Textbooks and reference materials

Introduction to Linear Algebra (5th edition) by Gilbert Strang
ISBN: 978-0980232776

Prerequisites

Basic operations of vectors and the relationships between vectors and 2- & 3-dimensional Euclidean spaces. Basics of exponential functions and differentiation. Basics of linear differential equations would be desirable.

Office hours and How to contact professors for questions

By appointment. Contact e-mail address: ikegami@shibaura-it.ac.jp

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Course that cultivates an ability for utilizing knowledge
Course that cultivates a basic problem-solving skills

Active-learning course

About half of the classes are interactive

Course by professor with work experience

Work experience	Work experience and relevance to the course content if applicable
N/A	N/A

Education related SDGs:the Sustainable Development Goals

4.QUALITY EDUCATION

Last modified : Sat Sep 09 05:25:51 JST 2023