Course detail
Matrices and tensors calculus
FEKT-LMATAcad. year: 2010/2011
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.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Kolman, B., Introductory Linear Algebra, Macmillan Publ. Comp., New York 1991.
Recommended reading
Classification of course in study plans
- Programme EEKR-ML Master's
branch ML-SVE , 2 year of study, summer semester, theoretical subject
branch ML-SVE , 1 year of study, summer semester, theoretical subject
branch ML-KAM , 2 year of study, summer semester, theoretical subject
branch ML-KAM , 2 year of study, summer semester, theoretical subject
branch ML-TIT , 2 year of study, summer semester, theoretical subject
branch ML-TIT , 1 year of study, summer semester, theoretical subject
branch ML-EVM , 2 year of study, summer semester, theoretical subject
branch ML-EVM , 1 year of study, summer semester, theoretical subject
branch ML-EST , 2 year of study, summer semester, theoretical subject
branch ML-EST , 1 year of study, summer semester, theoretical subject
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
Determinant of quadratic complex matrix.
Operations with matrices. Special types of matrices. Inverse matrix.
Matrix solutions of linear algebraic equations.
Linear, bilinear and quadratic forms. Definite of quadratics forms.
Spectral attributes of matrices.
Linear space, dimension.
Linear transform of coordinates of vector.
Covariant and contravariant coordinates of vector.
Definition of tensor.
Covariant, contravariant and mixed tensor.
Operation with tensors.
Symmetry and antisymmetry of tensors of second order.
Fundamentals seminar
Teacher / Lecturer
Syllabus
Determinant of quadratic complex matrix.
Operations with matrices. Special types of matrices. Inverse matrix. Matrices solutions of linear algebraic equations.
Linear, bilinear and quadratic forms. Definite of quadratics forms.
Spectral attributes of matrices.
Linear space, dimension.
Linearn transformations of coordinates of vector.
Covariant and contravariant coordinates of vector.
Definition of tensor. Covariants, contravariants and mixed tensor.
Operations with tensors. Symmetry and antisymmetry of tensors of second order.
Exercise in computer lab
Teacher / Lecturer
Syllabus
Spectral properties of matrices.
Operations with tensors.