Title:

Matrices and Tensors Calculus

Code:MMAT (FEKT MMAT)
Ac.Year:2017/2018
Term:Summer
Curriculums:
ProgrammeBranchYearDuty
IT-MSC-2MBI-Elective
IT-MSC-2MBS-Elective
IT-MSC-2MGM-Elective
IT-MSC-2MIN-Elective
IT-MSC-2MIS-Elective
IT-MSC-2MMI-Elective
IT-MSC-2MMM-Elective
IT-MSC-2MPV-Elective
IT-MSC-2MSK-Elective
Language:Czech
Credits:5
Completion:accreditation+exam (written&verbal)
Type of
instruction:
Hour/semLecturesSem. ExercisesLab. exercisesComp. exercisesOther
Hours:2600188
 ExaminationTestsExercisesLaboratoriesOther
Points:70200010
Guarantee:Kovár Martin, doc. RNDr., Ph.D., DMAT
Lecturer:Kovár Martin, doc. RNDr., Ph.D., DMAT
Instructor:Kovár Martin, doc. RNDr., Ph.D., DMAT
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Mathematics FEEC BUT
 
Learning objectives:
  Master the bases of the matrices and tensors calculus and its applications.
Description:
  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 and competences:
  Mastering basic techniques for solving tasks and problems from the matrices and tensors calculus and its applications.
Study literature:
 
  1. Havel, V., Holenda, J.: Lineární algebra, SNTL, Praha 1984 (in Czech).
  2. Hrůza, B., Mrhačová, H.: Cvičení z algebry a geometrie. Ediční stř. VUT 1993, skriptum (in Czech).
  3. Schmidtmayer J.: Maticový počet a jeho použití, SNTL, Praha, 1967 (in Czech).
  4. Boček, L.: Tenzorový počet, SNTL Praha 1976 (in Czech).
  5. Angot A.: Užitá matematika pro elektroinženýry, SNTL, Praha 1960 (in Czech).
  6. Kolman, B.: Elementary Linear Algebra, Macmillan Publ. Comp., New York 1986.
  7. Kolman, B.: Introductory Linear Algebra, Macmillan Publ. Comp., New York 1991.
  8. Gantmacher, F. R.: The Theory of Matrices, Chelsea Publ. Comp., New York 1960.
  9. Demlová, M., Nagy, J.: Algebra, STNL, Praha 1982 (in Czech).
  10. Plesník J., Dupačová, J., Vlach M.: Lineárne programovanie, Alfa, Bratislava , 1990 (in Slovak).
  11. Mac Lane, S., Birkhoff, G.: Algebra, Alfa, Bratislava, 1974 (in Slovak).
  12. Mac Lane, S., Birkhoff, G.: Prehľad modernej algebry, Alfa, Bratislava, 1979 (in Slovak).
  13. Krupka D., Musilová J.: Lineární a multilineární algebra, Skriptum Př. f. MU, SPN, Praha, 1989 (in Czech).
  14. Procházka, L. a kol.: Algebra, Academia, Praha, 1990 (in Czech).
    Halliday, D., Resnik, R., Walker, J.: Fyzika, Vutium, Brno, 2000 (in Czech).
  15. Crandal, R. E.: Mathematica for the Sciences, Addison-Wesley, Redwood City, 1991.
  16. Davis, H. T., Thomson, K. T.: Linear Algebra and Linear Operators in Engineering, Academic Press, San Diego, 2007.
  17. Mannuci, M. A., Yanofsky, N. S.: Quantum Computing For Computer Scientists, Cambridge University Press, Cabridge, 2008.
  18. Nahara, M., Ohmi, T.: Quantum Computing: From Linear Algebra to Physical Realizations, CRC Press, Boca Raton, 2008.
  19. Griffiths, D.: Introduction to Elementary Particles, Wiley WCH, Weinheim, 2009.
Progress assessment:
  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.
Exam prerequisites:
  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.