We generalize the nullity theorem of Gustafson [Linear Algebra Appl. (1984)]
from matrix inversion to principal pivot transform. Several special cases of
the obtained result are known in the literature, such as a result concerning
local complementation on graphs. As an application, we show that a particular
matrix polynomial, the so-called nullity polynomial, is invariant under
principal pivot transform.Comment: 5 pages, no figure
