Introduction to Algebra

The course cannot be taken simultaneously with:

Lineární algebra (AD7B01LAG)

Lecturer:

Petr Olšák

Tutor:

Petr Olšák

Supervisor:

Department of Mathematics

Synopsis:

The course covers introductory topics of linear algebra. They include matrices, matrix operations, inversion of matrices, vector spaces, bases and dimension and their applications to solving systems of linear equations. Vector spaces are presented over real numbers and GF(2). Eigenvalues and eigenvectors of matrices.

Requirements:

To be specified in seminars by tutors.

Syllabus of lectures:

1. Vector spaces, axioms of linearity.

2. Linear independence, linear dependence, linear span.

3. Basis, dimension, coordinates of vectors.

4. Matrices, operations with matrices.

5. Determinants.

6. Inverse matrices.

7. Systems of linear equations.

8. Linear mappings, matrices of linear mappings.

9. Eigenvalues and eigenvectors of matrices.

10. Scalar product, orthogonality.

11. Arithmetic vectors over GF(2), solution of linear equations over FG(2).

12. Applications in linear coding.

13. Back-up class.

Syllabus of tutorials:

1. Polynomials, roots of polynomials.

2. Gaussian elimination, rank of matrices.

3. Vector spaces, linear independence, linear dependence.

4. Basis, dimension, coordinates of vectors.

5. Matrices, operations with matrices.

6. Determinants.

7. Systems of linear equations.

8. Linear mappings, matrices of linear mappings.

9. Eigenvalues and eigenvectors of matrices.

10. Scalar product, orthogonality.

11. Arithmetic vectors over GF(2), solution of linear equations over FG(2).

12. Applications in linear coding.

13. Back-up class.

Study Objective:

Study materials:

1. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.

2. P. Pták: Introduction to Linear Algebra, starší vydání přístupné elektronicky.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Inteligentní systémy (compulsory course)
• Manažerská informatika (compulsory course)
• Softwarové inženýrství (compulsory course)
• Společný 1. ročník (compulsory course)
• Web a multimedia (compulsory course)
• Inteligentní systémy (STM-A7B-přechodné) (compulsory course)
• Manažerská informatika (STM-A7B-přechodné) (compulsory course)
• Web a multimedia (STM-A7B-přechodné) (compulsory course)
• Softwarové inženýrství (STM-A7B-přechodné) (compulsory course)