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Nonnegative and positive definiteness of matrices modified by two matrices of rank one. (English) Zbl 0728.15011
From the authors’ summary: Necessary and sufficient conditions are given for the nonnegative and positive definiteness of matrices of the form \(A- a_ 1a^*_ 1-a_ 2a^*_ 2\) and \(A+a_ 1a^*_ 1-a_ 2a^*_ 2\), where A is a Hermitian matrix and \(a_ 1,a_ 2\) are complex vectors.

15B57 Hermitian, skew-Hermitian, and related matrices
15B48 Positive matrices and their generalizations; cones of matrices
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