The question of which partial Hermitian matrices (some entries specified, some free) may be completed to positive definite matrices is addressed. It is shown that if the diagonal entries are specified and principal minors, composed of specified entries, are positive, then, if the undirected graph of the specified entries is chordal, a positive definite completion necessarily exists. Furthermore, if this graph is not chordal, then examples exist without positive definite completions. In case a positive definite completion exists, there is a unique matrix, in the class of all positive definite completions, whose determinant is maximal, and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original

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Pregnancy is generally described as a period with a high incidence of common mental disorders (CMD) in the life cycle of many women who incur the risk of developing mental problems including depression, post-traumatic stress and drug abuse. Our objective with this study was to gauge how the presence of violence in Portuguese pregnant women affected their psychopathology. One hundred and eighty-four pregnant outpatients of the Obstetrics and Gynaecology Department of the Hospital Pedro Hispano in Matosinhos, Oporto, Portugal with an average age of 29 and in their last 3 months of pregnancy were the subjects of this study. These participants were divided into two groups: one of abused women (n= 107) and another of non-abused women (n= 77). In order to be able to compare them, both groups were assessed with the Conflict Tactic Scale 2, the Brief Symptom Inventory and the Inventory of the Clinical Evaluation of Depression. It was observed that pregnant women who had suffered violence during pregnancy exhibited some form of CMD during pregnancy. Another important finding was the evidence of the negative impacts that domestic violence had on the mental health of women.