Czech

Not applicable.

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 Matematika 1 is required. The previous attendance to the subject Matematický seminář is warmly recommended.

Not applicable.

Teaching methods depend on the type of course unit as specified in the 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.

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.

Not applicable.

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.

Not applicable.

Not applicable.

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)
Kovár, M., Maticový a tenzorový počet, Skriptum, Brno, 2013, 220s. (CS)
Kovár, M., Selected Topics on Multilinear Algebra with Applications, Skriptum, Brno, 2015, 141s. (EN)

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)
Demlová, M., Nagy, J., Algebra, STNL, Praha 1982. (CS)
Havel, V., Holenda J.: Lineární algebra, SNTL, Praha 1984. (CS)