Minimisation of functions of a positive semidefinite matrix A subject to AX = 0 |
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Authors: | Bruce Calvert George AF Seber |
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Institution: | Mathematics Department, Auckland University, New Zealand |
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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. |
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Keywords: | 62H99 15A60 Positive semidefinite matrices maximum likelihood estimation projections in Hilbert space |
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