A NECESSARY AND SUFFICIENT CONDITION FOR A SYMMETRIC MATRIX TO BE A CORRELATION MATRIX

• Authors: Westa M.
• Languages of publication: PL

Abstracts

EN

Borowiecki, Kolupa and Kaliszyk (1984) and Dudek (2003) proposed methods in which the generalised Hellwig's inequality is used for verifying that a symmetric matrix, which has the following properties: (1) - all elements on the main diagonal are units; (2) -all elements outside the main diagonal are not greater than one in absolute value, is a correlation matrix of certain variables. The authoress (see forthcoming paper) showed that this verification procedure may improperly indicate the correlation matrices. The theorems proved in the present paper define various forms of the necessary and sufficient condition for a symmetric matrix with properties (1)-(2) to be a correlation matrix. Among others things, it was shown that any symmetric 3x3 matrix with properties (1)-(2) is a correlation matrix if and only if its determinant is non-negative. Some results obtained generalize those given by Hauke and Pomianowska (1987) for correlation pair.

Keywords

EN

CORRELATION MATRIX; GENERALISED HELLWIG'S INEQUALITY; HELLWIG'S INEQUALITY

Discipline

• ECONOMICS: ECONOMICS

• Publisher: Główny Urząd Statystyczny
• Journal: Przegląd Statystyczny
• Year: 2008
• Volume: 55
• Issue: 3
• Pages: 33-46
• Document type: ARTICLE

Contributors

author

Westa M.

• M. Westa, Uniwersytet Warminsko-Mazurski w Olsztynie, Wydzial Nauk Ekonomicznych, Katedra Metod Ilosciowych, ul. Oczapowskiego 4, 10-719 Olsztyn, Poland

Identifiers

CEJSH db identifier

08PLAAAA05249933