doc. RNDr. Martin Kovár, Ph.D.

Department of Mathematics (UMAT)

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

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.

Not applicable.

Not applicable.

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.
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.

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

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

English

Not applicable.

1. Matrices as algebraic structure. Matrix operations. Determinant.
2. Matrices in systems of linear algebraic equations.
3. Vector space, its basis and dimension. Coordinates and their transformation. Sum and intersection of vector spaces.
4. Linear mapping of vector spaces and its matrix representation.
5. Inner (dot) product, orthogonal projection and the best approximation element.
6. Eigenvalues and eigenvectors. Spectral properties of (especially Hermitian) matrices.
7. Bilinear and quadratic forms. Definitness of quadratic forms.
8. Linear forms and tensors. Verious types of coordinates. Covariant, contravariant and mixed tensors.
9. Tensor operations. Tensor and wedge products.Antilinear forms.
10. Matrix formulation of quantum. Dirac notation. Bra and Ket vectors. Wave packets as vectors.
11. Hermitian linear operator. Schrodinger equation. Uncertainty Principle and Heisenberg relation.
12. Multi-qubit systems and quantum entaglement. Einstein-Podolsky-Rosen experiment-paradox.
13. Quantum calculations. Density matrix. Quantum teleportation.

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

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.

• Programme AUDIO-PU Master's

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

• Programme EEKR-MN Master's

  branch MN-TIT , 1. year of study, summer semester, 5 credits, theoretical subject
  branch MN-KAM , 1. year of study, summer semester, 5 credits, theoretical subject
  branch MN-EVM , 1. year of study, summer semester, 5 credits, theoretical subject
  branch MN-EST , 1. year of study, summer semester, 5 credits, theoretical subject
  branch MN-SVE , 1. year of study, summer semester, 5 credits, theoretical subject
  branch MN-EEN , 1. year of study, summer semester, 5 credits, theoretical subject
  

• Programme AUDIO-PU Master's

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

8 hours, compulsory

doc. RNDr. Martin Kovár, Ph.D.

eLearning: currently opened course