Confidence regions in a multivariate regression model with constraints II
Conjugacy and factorization results on matrix groups
In this survey paper, we present (mainly without proof) a number of results on conjugacy and factorization in general linear groups over fields and commutative rings. We also present the additive analogue in matrix rings of some of these results. The first section deals with the question of expressing elements in the commutator subgroup of the general linear group over a field as (simple) commutators. In Section 2, the same kind of problem is discussed for the general linear group over a commutative...
Conjugacy for closed convex sets.
Conjunctively polynomial-like Boolean functions.
Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs
The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity. We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.
Conservative Quadratic Forms.
Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
L. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331 (2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformations A ↦ ˜S−1AS in which S is a nonsingular quaternion matrix and h = a + bi + cj + dk ↦ ˜h := a − bi + cj − dk (a, b, c, d ∈ ℝ). We give an analogous canonical form of a quaternion matrix with respect to consimilarity transformations A ↦^S−1AS in which h ↦ ^h is an arbitrary involutive automorphism of the...
Constrained Extrema of Bilinear Functionals.
Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs
Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.The author developed computer programs needed for the classification of designs with certain automorphisms by the local approach method. All these programs use canonicity test or/and construction of canonical form of an integer matrix. Their efficiency substantially influences the speed of the whole computation. The present paper deals with the implemented canonicity algorithm. It is based on ideas used by McKay, Meringer,...
Constructing copositive matrices from interior matrices.
Constructing matrix geometric means.
Constructing the maximal monoids in the semigroups , and
Constructions for type I trees with nonisomorphic Perron branches
A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between...
Constructions of trace zero symmetric stochastic matrices for the inverse eigenvalue problem.
Continued fractions and transformations of integer sequences.
Continuite lipschitzienne du spectre comme fonction d'un opérateur normal
Controllability, Bezoutian and relative primeness.
Controllability in the max-algebra
We are interested here in the reachability and controllability problems for DEDS in the max-algebra. Contrary to the situation in linear systems theory, where controllability (resp observability) refers to a (linear) subspace, these properties are essentially discrete in the -linear dynamic system. We show that these problems, which consist in solving a -linear equation lead to an eigenvector problem in the -algebra. More precisely, we show that, given a -linear system, then, for every natural...
Controllability of linear impulsive systems – an eigenvalue approach
This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation...
Controllability of partially prescribed matrices.