Linear Algebra I

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Brezina Jan 
Lecture2  Exercise0  Experiment0
Syllabus updated
Lecture notes updated
Spring Semester  /  Recommended semester:1

Outline of lecture

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.

Purpose of lecture

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

Plan of lecture

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.

Textbook and reference

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.

Related and/or prerequisite courses

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).

Comments from lecturer

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

Contact Information

Email : brezinaツシ
Office : Room 219, Main Bldg., Ookayama Campus

TA information:
Name: Hiroki Murakami
Email: murakami.h.ahツシ
Office: H316

Office Hours

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

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