Course detail

Matrices and tensors calculus

FEKT-MPA-MATAcad. year: 2026/2027

Not applicable.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Martin Kovár, Ph.D.

Department

Faculty of Electrical Engineering and Communication (FEKT)

Entry knowledge

Not applicable.

Rules for evaluation and completion of the course

The semester examination is rated at a maximum of 70 points.  It is possible to get a maximum of 30 points in practices, 20 of which are for written tests and 10 points for 2 project solutions, 5 points of each.
The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year. 

Aims

Not applicable.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Kolman, B., Elementary Linear Algebra, Macmillan Publ. Comp., New York, ISBN 978-0029463703, 1986. (EN)
Kolman, B., Hill, D. R., Introductory Linear Algebra, Pearson, New York, 978-8131723227, 2008. (EN)

Recommended reading

Crandal, R. E., Mathematica for the Sciences, Addison-Wesley, Redwood City, ISBN 978-0201510010, 1991. (EN)
Davis, H. T., Thomson K. T., Linear Algebra and Linear Operators in Engineering, Academic Press, San Diego, ISBN 978-0122063497, 2007. (EN)

Classification of course in study plans

  • Programme MPA-NCP Master's 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. RNDr. Martin Kovár, Ph.D.

Syllabus

Matrices and matrix operations. Determinants. Systems of linear equations. Vector spaces, bases, dimensions, and coordinate transformations. Operations with vector spaces – sum, intersection, and linear mappings. Inner product, orthogonal projection, and best approximation. Eigenvalue problem. Spectral properties of matrices. Bilinear and quadratic forms, definiteness of quadratic forms. Linear forms and tensors. Different types of tensors and coordinate systems. Operations with tensors – tensor product and outer product. Physical applications – Lorentz transformation and matrix quantum mechanics. 

Individual preparation for excercises

26 hours, optionally

Teacher / Lecturer

doc. RNDr. Martin Kovár, Ph.D.

Syllabus

Independent study of materials related to the exercise; preparation of calculations, designs, and procedures for practical tasks; study of instructions and technical documentation; continuous preparation for knowledge assessment.

 

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

doc. RNDr. Martin Kovár, Ph.D.

Syllabus

Matrices and matrix operations. Determinants. Systems of linear equations. Vector spaces, bases, dimensions, and coordinate transformations. Operations with vector spaces – sum, intersection, and linear mappings. Inner product, orthogonal projection, and best approximation. Eigenvalue problem. Spectral properties of matrices. Bilinear and quadratic forms, definiteness of quadratic forms. Linear forms and tensors. Different types of tensors and coordinate systems. Operations with tensors – tensor product and outer product.

 

Individual preparation for a final exam

30 hours, optionally

Teacher / Lecturer

doc. RNDr. Martin Kovár, Ph.D.

Syllabus

Independent review and systematization of the topics covered during the semester; study of course materials; practice of theoretical knowledge and practical skills; solving sample tasks and comprehensive preparation for the final examination.

 

Project

12 hours, compulsory

Teacher / Lecturer

doc. RNDr. Martin Kovár, Ph.D.

Syllabus

Independent project work aimed at applying and developing acquired knowledge and skills. Problem analysis, design and implementation of the solution, verification of results, and preparation and presentation of the achieved outcomes.