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Bordered matrices and some their applications

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Kolupa M., Śleszyński Z.
Central European Review of Economics & Finance
|
2011
|
issue Vol. 1, No 1
44-50
EN
In this paper bordered matrices and some their applications are presented. In particular we give information how can be found matrix F = AB-1C without calculation the inverse of matrix B (when B = I this way we obtain Cauchy's product of matrices A and C). We present how to find generalized inverse of the Moore'a-Penrose'a type too and finally calculate value of determinant of given matrix A of order nxn.(original abstract)
2

Krzysztof Malaga, Karolina Sobczak, Mikroekonomia. Ujęcie statyczne i dynamiczne, Wydawnictwo C.H. Beck, Warszawa 2020, 420 ss.

100%
Lach Ł.
Ekonomista
|
2021
|
issue 5
706-709
3
Content available remote

Kritická místa v matematice u českých žáků na základě výsledků šetření TIMSS 2007

85%
Rendl M., Vondrová N.
Pedagogická orientace (Journal of the Czech Pedagogical Society)
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2014
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vol. 24
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issue 1
22-57
EN
The goal of the empirical study is to describe critical areas of primary mathematics as can be found from the Czech Grade 8 pupils’ results in TIMSS 2007 and to identify possible causes of their difficulty for pupils. In the first part, a research background is briefly given – international comparative research in mathematics and possibilities of the secondary analyses of its data. The second part describes methodology in detail. We analysed data from so called TIMSS almanacs (results of Czech pupils at the level of concrete mathematical items from TIMSS and answers of the teacher questionnaire). To interpret possible causes we also used curricular documents and the analysis of the apparently most used primary mathematics textbooks. We set up a criterion for deciding whether the Czech pupils’ results for the given item is below their standard which we determined by comparing their average success rate with that of the international sample. Thus so called weak and very weak items were identified. They were divided into three areas which can be considered critical areas for Czech pupils: Algebra (with subareas of Functions, Substitution, Equations and inequalities, Expressions), Sequences, Shapes and solids. For each of the areas, weak and very weak items are presented together with their results and an outline of the nature of their difficulty for Czech pupils and possible causes of Czech pupils’ failure to solve them. It transpires that it is necessary to get a deeper insight into the nature of problems by clinical interviews with pupils. This will be a topic of further articles.
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