Computing the determinants by reducing the orders by four.
Computing the numerical range of Krein space operators
Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined...
Computing tournament sequence numbers efficiently with matrix techniques.
Concentration of the spectral measure for large matrices.
Concentration of the spectral measure for large random matrices with stable entries.
Concentration of the spectral measure of large Wishart matrices with dependent entries.
Concerning Colimits in the Category of Noncommutative Algebras
Condition numbers of Hessenberg companion matrices
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition number than...
Condition numbers of the Krylov bases and spaces associated with the truncated iteration.
Conditioning properties of the stationary distribution for a Markov chain.
Conditions for a totally positive completion in the case of a symmetrically placed cycle.
Cones of polynomials
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.