Row equivalence, equivalence, and similarity of matrices are studied; some problems concerning an extension of these relations to infinite matrices are discussed.
As indicated by the title, this thesis generalizes the Main Inertia
Theorem of Ostrowski and Schneider [8]. The first three results
concern the formation of a polynomial function f(A, A*, H) so that
the existence of an hermitian H for which f(A, A*, H) is positive
definite is a necessary...
The author studies the class of rectangular arrangements in
terms of two binary relations on the objects of the arrangement.
He shows how a univalent matrix determines a unique rectangular
arrangement, and how each rectangular arrangement is associated
with one, two, or four distinct matrices, according to the number
of...
In this paper we investigate the Lyapunov mapping
P --> AP + PA *
where A is a positive stable matrix and P is a hermitian
matrix. In particular, for special positive stable A we
characterize the image of the cone of positive definite matrices
under this mapping. In Section...
This paper studies necessary and sufficient conditions for
a matrix to be conjunctive with its adjoint. The problem is solved
completely in the usual complex case, in which it is shown that a
matrix is conjunctive to its adjoint iff it is conjunctive to a real
matrix. The problem is...