Course title
Linear Algebra
Course description
We will conduct online teaching in Spring 2021.
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, you 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 as well as solve the linear differential equation given by A.
A-1
5. The students can determine the corresponding linear transformation given a change of basis of a vector space.
A-1
Language
English
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. 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
Work on homework problems 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
Work on homework problems 220分
3. Transposes and permutations
Vector spaces and subspaces
Review the content of the lecture (2.7, 3.1 in the textbook) 120分
Work on homework problems 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
Work on homework problems 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
Work on homework problems 220分
6. Orthogonality
Projections and subspaces
Review the content of the lecture (4.1-4.2 in the textbook) 120分
Work on homework problems 240分
7. Mid-term presentation and discussions on the solutions afterwards Preparation for the mid-term presentation 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
Work on homework problems 240分
9. Properties of determinants
Formulas for determinants
Review the content of the lecture (5.1-5.2 in the textbook) 160分
Work on homework problems 220分
10. Applications of determinants
Eigenvalues and eigenvectors
Review the content of the lecture (5.3, 6.1 in the textbook) 160分
Work on homework problems 220分
11. Diagonalization
Differential equations
Review the content of the lecture (6.2-6.3 in the textbook) 160分
Work on homework problems 220分
12. Symmetric matrices
Positive definite matrices
Review the content of the lecture (6.4-6.5 in the textbook) 160分
Work on homework problems 220分
13. Linear transformations
Choice of basis
Review the content of the lecture (8.1-8.3 in the textbook) 160分
Work on homework problems 220分
14. Final exam and discussions on the solutions afterwards Preparation for the final exam 380分
Total. - - 5300分
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Homework Mid-term presentation Final exam Total.
1. 20% 4% 5% 29%
2. 15% 4% 5% 24%
3. 10% 4% 3% 17%
4. 10% 3% 10% 23%
5. 0% 0% 7% 7%
Total. 55% 15% 30% -
Evaluation method and criteria
Those who get at least 60% of the full score will pass this course.
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