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

Bruce Calvert and George A. F. Seber

Journal of Multivariate Analysis, 1978, vol. 8, issue 2, 274-281

Abstract: 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.

Keywords: Positive; semidefinite; matrices; maximum; likelihood; estimation; projections; in; Hilbert; space (search for similar items in EconPapers)
Date: 1978
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