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Matrix Algebra in Statistics
Navrátil, František ; Kulich, Michal (advisor) ; Antoch, Jaromír (referee)
of the bachelor thesis Title: Matrix Algebra in Statistics Author: František Navrátil Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Mgr. Michal Kulich Ph.D. Abstract: The thesis deals with the theory of matrix algrebra, which is applicable in probability and statistics. The aim of the thesis is to summarize it in a clear and understandable way, so that the student familiar with the basics of matrix theory can expand his knowledge and use it in further studies. Therefore, the thesis contains many definitions and proved theorems, and examples to help understanding the theory. Applications are mentioned. It also provides references for further reading. The thesis begins with a brief summary of basic definitions and results in matrix algebra, which are covered in the usual courses on linear algebra. Subsequent chapters are specific, inter alia, for probability and statistics - in particular, they focus on special types of matrices and their properties, important matrix decompositions, functions of matrices and matrix difierentiation. Keywords: matrix algebra, statistics, idempotent matrix, spectral decomposition, Kronecker product
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Matrix Algebra in Statistics
Navrátil, František ; Kulich, Michal (advisor) ; Antoch, Jaromír (referee)
of the bachelor thesis Title: Matrix Algebra in Statistics Author: František Navrátil Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Mgr. Michal Kulich Ph.D. Abstract: The thesis deals with the theory of matrix algrebra, which is applicable in probability and statistics. The aim of the thesis is to summarize it in a clear and understandable way, so that the student familiar with the basics of matrix theory can expand his knowledge and use it in further studies. Therefore, the thesis contains many definitions and proved theorems, and examples to help understanding the theory. Applications are mentioned. It also provides references for further reading. The thesis begins with a brief summary of basic definitions and results in matrix algebra, which are covered in the usual courses on linear algebra. Subsequent chapters are specific, inter alia, for probability and statistics - in particular, they focus on special types of matrices and their properties, important matrix decompositions, functions of matrices and matrix difierentiation. Keywords: matrix algebra, statistics, idempotent matrix, spectral decomposition, Kronecker product
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Fractal simplex algorithm in VBA
Ouzký, Karel ; Pelikán, Jan (advisor) ; Fábry, Jan (referee)
Basic idea of fractal simplex algorithm is based in the theory of matrix counting and knowledge of matrix representation of simplex tabuleao from revised simplex method. My desire is to explain theoretical basics on which this algorithm works and provide solution in language Visual Basic for Applications in application MS Excel 2007. Main benefit I see in the fact, that algorithm can solved specific class of mathematical problems in a way of exactness counting whithout necessity of using decimal numbers.
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