Course detail

# Matrices and tensors calculus

Definition of matrix. Fundamental notions. Equality and inequality of matrices. Transposition of matrices. Special kinds of matrices. Determinant, basic attributes. Basic operations with matrices. Special types of matrices. Linear dependence and indenpendence. Order and degree of matrices. Inverse matrix.
Solutions of linear algebraic equations. Linear and quadratic forms. Spectral attributes of matrices, eigen-value, eigen-vectors and characteristic equation. Linear space, dimension. báze. Linear transform of coordinates of vector.
Covariant and contravariant coordinates of vectors and their transformations. Definition of tensor. Covariant, contravariant and mixed tensor. Operation on tensors. Sum of tensors. Product of tensor and real number. Restriction of tensors. Symmetry and antisymmetry of tensors.

Learning outcomes of the course unit

Mastering basic techniques for solving tasks and problems from the matrices and tensors calculus and its applications.

Prerequisites

The knowledge of the content of the subject BMA1 Matematika 1 is required. The previous attendance to the subject BMAS Matematický seminář is warmly recommended.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Havel V., Holenda J.: Lineární algebra, SNTL, Praha 1984.
Hrůza B., Mrhačová H.: Cvičení z algebry a geometrie. Ediční stř. VUT 1993, skriptum
Schmidtmayer J.: Maticový počet a jeho použití, SNTL, Praha, 1967.
Boček L.: Tenzorový počet, SNTL Praha 1976.
Angot A.: Užitá matematika pro elektroinženýry, SNTL, Praha 1960.
Kolman, B., Elementary Linear Algebra, Macmillan Publ. Comp., New York 1986.
Kolman, B., Introductory Linear Algebra, Macmillan Publ. Comp., New York 1991.
Gantmacher, F. R., The Theory of Matrices, Chelsea Publ. Comp., New York 1960.
Demlová, M., Nagy, J., Algebra, STNL, Praha 1982.
Plesník J., Dupačová J., Vlach M., Lineárne programovanie, Alfa, Bratislava , 1990.
Mac Lane S., Birkhoff G., Algebra, Alfa, Bratislava, 1974.
Mac Lane S., Birkhoff G., Prehľad modernej algebry, Alfa, Bratislava, 1979.
Krupka D., Musilová J., Lineární a multilineární algebra, Skriptum Př. f. MU, SPN, Praha, 1989.
Procházka L. a kol., Algebra, Academia, Praha, 1990.
Halliday D., Resnik R., Walker J., Fyzika, Vutium, Brno, 2000.
Crandal R. E., Mathematica for the Sciences, Addison-Wesley, Redwood City, 1991.
Davis H. T., Thomson K. T., Linear Algebra and Linear Operators in Engineering, Academic Press, San Diego, 2007.
Mannuci M. A., Yanofsky N. S., Quantum Computing For Computer Scientists, Cambridge University Press, Cabridge, 2008.
Nahara M., Ohmi T., Quantum Computing: From Linear Algebra to Physical Realizations, CRC Press, Boca Raton, 2008.
Griffiths D. Introduction to Elementary Particles, Wiley WCH, Weinheim, 2009.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Requirements for completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every.

Language of instruction

Czech

Work placements

Not applicable.

Aims

Master the bases of the matrices and tensors calculus and its applications.

Specification of controlled education, way of implementation and compensation for absences

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.

Classification of course in study plans

• Programme AUDIO-P Master's

branch P-AUD , 1. year of study, summer semester, 5 credits, optional interdisciplinary

• Programme EEKR-M Master's

branch M-TIT , 1. year of study, summer semester, 5 credits, theoretical subject

• Programme EEKR-M1 Master's

branch M1-TIT , 1. year of study, summer semester, 5 credits, theoretical subject
branch M1-KAM , 1. year of study, summer semester, 5 credits, theoretical subject

• Programme EEKR-M Master's

branch M-KAM , 1. year of study, summer semester, 5 credits, theoretical subject
branch M-EVM , 1. year of study, summer semester, 5 credits, theoretical subject

• Programme EEKR-M1 Master's

branch M1-EVM , 1. year of study, summer semester, 5 credits, theoretical subject
branch M1-EST , 1. year of study, summer semester, 5 credits, theoretical subject

• Programme EEKR-M Master's

branch M-EST , 1. year of study, summer semester, 5 credits, theoretical subject
branch M-SVE , 1. year of study, summer semester, 5 credits, theoretical subject

• Programme EEKR-M1 Master's

branch M1-SVE , 1. year of study, summer semester, 5 credits, theoretical subject

• Programme EEKR-M Master's

branch M-EEN , 1. year of study, summer semester, 5 credits, theoretical subject

• Programme EEKR-M1 Master's

branch M1-EEN , 1. year of study, summer semester, 5 credits, theoretical subject

• Programme AUDIO-P Master's

branch P-AUD , 2. year of study, summer semester, 5 credits, optional interdisciplinary

• Programme EEKR-M Master's

branch M-TIT , 2. year of study, summer semester, 5 credits, theoretical subject
branch M-EST , 2. year of study, summer semester, 5 credits, theoretical subject
branch M-SVE , 2. year of study, summer semester, 5 credits, theoretical subject

• Programme EEKR-CZV lifelong learning

branch ET-CZV , 1. year of study, summer semester, 5 credits, theoretical subject

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Exercise in computer lab

18 hours, compulsory

Teacher / Lecturer

The other activities

8 hours, compulsory

Teacher / Lecturer