Almost skew-symmetric matrices (Q1880982)

It is shown that almost skew-symmetry is invariant under a principal pivot transform and inversion, and that the symmetric parts of Schur complements in almost skew-symmetric matrices have at most rank one. Affine combinations of \(A\) and \(A^{t}\) are also used to gain further insight into eigenvalue location and the numerical range of an almost skew-symmetric matrix.