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...
Row equivalence, equivalence, and similarity of matrices are studied; some problems concerning an extension of these relations to infinite matrices are discussed.
This thesis has four main results. First we find a reduction form
for symmetric matrices over fields of characteristic two. This result
parallels the diagonalization theorem for symmetric matrices over
fields of characteristic not two.
Secondly we reduce our reduction form to a canonical form in
perfect fields of characteristic...
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 thesis we consider computer techniques for inverting
n X n matrices and linear Fredholm integral operators of the
second kind. We develop techniques which allow us to prove the
existence of and find approximations to inverses for the above
types of operators. In addition, we are able to...
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...
A method for the synthesis of bilateral networks is
presented. A new algorithm for the realization of basic
cut-set matrices is developed. This is done by the
following procedure:
1) We form submatrices, M[subscript j] (i), j= 1,2,..., of the
given cut-set matrix, such that M[subscript j](i) satisfies
the properties...
This paper is a continuation of William Zell's thesis, A Model of Non-Euclidean Geometry in Three Dimensions. The purpose of that thesis was to show that the axioms of non-Euclidèan geometry are consistent if Euclidean geometry an& hence arithrnetic is consistent. Mr. Zell. discussed the axioms of connection and order...