Course title
M20170001
Linear Algebra

 KUNO Erika
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
先進国際課程 A-1 A-1 Students shall obtain basic and advanced knowledge and skills in mathematics, natural and computer sciences as well as presentation skills to communicate on their knowledge with scholars from various fields.
(改組前)先進国際課程 A-1 A-1 Students shall obtain basic and advanced knowledge and skills in mathematics, natural and computer sciences as well as presentation skills to communicate on their knowledge with scholars from various fields.
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.
Course description
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.
Goals and objectives
  1. The students can use basic operations of matrices to solve a linear equation with Gaussian elimination.
  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.
  3. The students can use Gram-Schmidt to find an orthonormal basis for a given subspace of a vector space.
  4. The students can use eigenvariables ＆ eigenvectors of a given matrix A to diagonalize A and to compute the power of A.
  5. The students can raise concrete examples of a linear transformation and can determine whether a given transformation is linear or not.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Final exam Total.
1. 30% 30%
2. 30% 30%
3. 15% 15%
4. 15% 15%
5. 10% 10%
Total. 100% -
Evaluation method and criteria
Final exam will contribute 100% of your grade.
Those who get at least 60% of the full score will pass this course.
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) 160minutes
Preparation before the lecture 220minutes
2. Matrix operations and inverses
Elimination and factorization 		Review the content of the lecture (2.4-2.6 in the textbook) 160minutes
Preparation before the lecture 220minutes
3. Transposes
Vector spaces and subspaces 		Review the content of the lecture (2.7, 3.1 in the textbook) 120minutes
Preparation before the lecture 260minutes
4. The nullspace
The complete solution to Ax = b 		Review the content of the lecture (3.2-3.3 in the textbook) 160minutes
Preparation before the lecture 220minutes
5. Basis and dimension
The four fundamental subspaces 		Review the content of the lecture (3.4-3.5 in the textbook) 160minutes
Preparation before the lecture 220minutes
6. Orthogonality
Projections and subspaces 		Review the content of the lecture (4.1-4.2 in the textbook) 160minutes
Preparation before the lecture 220minutes
7. Review Work on exercises 160minutes
Preparation before the lecture 220minutes
8. Least squares approximations
Orthonormal bases and Gram-Schmidt 		Review the content of the lecture (4.3-4.4 in the textbook) 160minutes
Preparation before the lecture 220minutes
9. Properties of determinants
Formulas for determinants 		Review the content of the lecture (5.1-5.2 in the textbook) 160minutes
Preparation before the lecture 220minutes
10. Applications of determinants
Eigenvalues and eigenvectors 		Review the content of the lecture (5.3, 6.1 in the textbook) 160minutes
Preparation before the lecture 220minutes
11. Diagonalization Review the content of the lecture (6.2 in the textbook) 160minutes
Preparation before the lecture 220minutes
12. Linear transformations
The Matrix of a Linear Transformation 		Review the content of the lecture (8.1, 8.2 in the textbook) 160minutes
Preparation before the lecture 220minutes
13. Review Work on exercises 160minutes
Preparation before the lecture 220minutes
14. Final exam and discussions on the solutions afterwards Preparation for ＆ Review of the final exam 380minutes
Total. - - 5320minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
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.
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 Mar 14 13:24:52 JST 2026