- School of Science
- School of Engineering
- Group 2
- Group 3
- Group 4
- Group 5
- Group 6
- Metallurgical Engineering
- Organic and Polymeric Materials
- Inorganic Materials
- Chemical Engineering Course
- Chemical Engineering Course(Chemical Engineering)
- Applied Chemistry Course(Chemical Engineering)
- Polymer Chemistry
- Mechanical Engineering and Science
- Mechanical and Intelligent Systems Engineering
- Mechano-Aerospace Engineering
- International Development Engineering
- Control and Systems Engineering
- Industrial and Systems Engineering
- Electrical and Electronic Engineering
- Computer Science
- Civil Engineering
- Architecture and Building Engineering
- Social Engineering
- Common Cource of Engineering

- School of Bioscience and Biotechnology
- Common Course of Undergraduate School

- Graduate School of Science and Engineering
- Mathematics
- Physics(Particle- Nuclear- and Astro-Physics)
- Physics(Condensed Matter Physics)
- Chemistry
- Earth and Planetary Sciences
- Chemistry and Materials Science
- Metallurgy and Ceramics Science
- Organic and Polymeric Materials
- Applied Chemistry
- Chemical Engineering
- Common Course of Mechanical Engineering
- Mechanical Sciences and Engineering
- Mechanical and Control Engineering
- Mechanical and Aerospace Engineering
- Common Course of Electronic Engineering
- Electrical and Electronic Engineering
- Physical Electronics
- Communications and Integrated Systems
- Communications and Computer Engineering
- Civil Engineering
- Architecture and Building Engineering
- International Development Engineering
- Nuclear Engineering

- Graduate School of Bioscience and Biotechnology
- Interdisciplinary Graduate School of Science and Engineering
- Built Environment
- Energy Sciences
- Computational Intelligence and Systems Science
- Electronic Chemistry
- Materials Science and Engineering
- Innovative and Engineered Materials
- Environmental Chemistry and Engineering
- Environmental Science and Technology
- Mechano-Micro Engineering
- Information Processing
- Electronics and Applied Physics

- Graduate School of Information Science and Engineering
- Graduate School of Decision Science and Technology
- Graduate School of Innovation Management
- Common Course of Graduate School
- Program for Leading Graduate Schools

- Lecturer
- Brezina Jan

- Place
- Wed1-2(H104)

- Credits
- Lecture2 Exercise0 Experiment0

- Code
- 1121

- Syllabus updated
- 2015/5/20

- Lecture notes updated
- 2015/6/8

- Semester
- Spring Semester / Recommended semester:1

In Linear Algebra I we introduce numerical vectors and matrices which are indispensable tools of modern computation and thinking. We learn and practice calculation. The idea of linear algebra is to take known geometrical objects, describe them algebraically and create rules for calculation. Computers could not work without linear algebra and so you can't either.

To develop and strengthen the understanding of what was is linear algebra and how to successfully use it in other technical subjects.

1. Vectors, numerical vectors, matrices.

2. Identity matrix, symmetric matrices, diagonal matrices, triangular matrices.

3 Operations with matrices.

4. Invertible matrices and inverse matrix.

5. System of linear equations and Gaussian elimination.

6. Elementary operations and elementary matrices.

7. General solution of system of linear equations.

8. Method for calculating an inverse matrix.

9. Rank of matrices.

10. Definition of determinant(up to 3ﾃ3 matrices), geometrical meaning of determinant.

11. Definition of determinant(from 4ﾃ4 matrices) (permutations), multilinearity (adding rows, multiplying by constant), alternating sign (interchange of rows).

12. Methods for calculating determinant, special determinant (triangular matrix, Vandermonde determinant) .

13. Laplace expansion of determinant

14. Determinant of transposed matrix and product of matrices.

15. Cramer's formula, formula for inverse matrices.

We will follow "Linear Algebra: A Modern Introduction" by David Poole, 3rd or newer edition. This book will be also used in Linear Algebra II in winter. You are not required to buy it, but it would definitely help you.

You can compare with any English or Japanese textbook on introduction to linear algebra you find online or in the library. The main topics are always the same.

You should register together with the course "Exercise in Linear Algebra I (Course No. 1331)".

Based on the results of tests, mid-term exam and final exam. Also your work during semester counts. Details to be explained on first lecture (see content of the first class).

The course will contain the same amount of mathematical knowledge as Japanese courses, but with the advantage of learning mathematical English.

Email : brezinaﾂｼmath.titech.ac.jp

Office : Room 219, Main Bldg., Ookayama Campus

TA information:

Name: Hiroki Murakami

Email: murakami.h.ahﾂｼm.titech.ac.jp

Office: H316

Setup a meeting time after class or by an email first.