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...
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...
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...
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 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...
Row equivalence, equivalence, and similarity of matrices are studied; some problems concerning an extension of these relations to infinite matrices are discussed.
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...