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 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...
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...
Neutron flux and gamma-ray dose have been measured in the
experimental facilities of the Oregon State TRIGA reactor.
Thermal neutron flux measurements utilized foil activation
techniques.
The gamma-ray dose was measured with a thermoluminescent
dosimetry system. The thermoluminescent material used was LiF.
Fast neutron spectrum measurements were performed. The
fast...
Let A be an n x n real, symmetric matrix with distinct characteristic values λ₁, λ₂,...,λɴ. Then there exists an orthogonal matrix P such that PAPᵀ = Λ = (λi). Given a small symmetric change, ∆A, in the matrix A, we can calculate the resulting changes, ∆P, and ∆Λ, in...
Nonnegative matrices have a myriad of applications in the biological, social, and physical genres. Of particular importance are the primitive matrices. A nonnegative matrix, M, is primitive exactly when there is a positive integer, k, such that M[superscript k] has only positive entries; that is, all the entries in M[superscript...