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Lecturer(s)
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Fišerová Eva, doc. RNDr. Ph.D.
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Course content
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Row and column spaces of a matrix, subspaces and orthogonal complement. Projector operators. Matrices of full rank. Generalized inverse, consistent linear equations, reflexive g-inverse. g-Inverse for a minimum norm solution of linear system, g-inverse for a least squares solution, g-inverse for minimum norm least squares solution. Solution of matrix equations. g-Inverse of partitioned matrices. Projectors and their properties. Simultaneous reduction of a pair of Hermitian forms. Gauss-Markov model. Distribution of quadratic forms.
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Master essential tools for using of the linear algebra in mathematical statistics, especially using of g-inverse of matrices in solving estimation and testing problems.
Knowledge To know the theory of linear systems with a singular matrix and algorithms for determination different types of generalized matrix inverse.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject
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Recommended literature
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C. R. Rao, S. K. Mitra. (1971). Generalized inverse of matrices and its applications. John Willey & Sons, inc., New York, etc.
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J. R. Magnus and H. Neudecker. (1999). Matrix differential calculus with applications in statistics and econometrics. Revised edition. Chichester: Wiley.
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