Minimisation of functions of a positive semidefinite matrix A subject to AX = 0

A common problem in multivariate analysis is that of minimising or maximising a function f of a positive semidefinite matrix A subject possibly to AX = 0. Typically A is a variance-covariance matrix. Using the theory of nearest point projections in Hilbert spaces, it is shown that the solution satisfies the equation f'(A) + M - A = 0, where A = P0(M) and P0 is a certain projection operator.

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Year of publication:	1978
Authors:	Calvert, Bruce ; Seber, George A. F.
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 8.1978, 2, p. 274-281
Publisher:	Elsevier
Keywords:	Positive semidefinite matrices maximum likelihood estimation projections in Hilbert space

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005199512