The complexity of performing matrix computations, such as solving a linear system, inverting a nonsingular matrix or computing its rank, has received a lot of attention by both the theory and the scientific computing communities. In this paper we address some "nonclassical" matrix

On integer matrices obeying certain matrix equations

is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space---classical model selection

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding

are worth striving for. It is shown that these features can be obtained by constructing a matrix with a certain “Property U.” Matrices having this property are exhibited for the equations of steady and unsteady gasdynamics. In order to construct them, it is found helpful to introduce “parameter vectors

Abstract. The existence of non-trivial solutions X to matrix equations of the form

Abstract not found

Abstract. The existence of non-trivial solutions X to matrix equations of the form F (X,A1,A2, · · ·,As) = G(X,A1,A2, · · ·,As) over the real numbers is investigated. Here F and G denote monomials in the (n × n)-matrix X = (xij) of variables together with (n × n)-matrices A1,A2, · · ·,As

. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a first-order perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating

Abstract. We characterize discrete groups Γ ⊂ GL(n, R) which act properly discontinuously on the homogeneous space GL(m, R)\GL(n, R). A manifold M is called a complete locally homogeneous if M = J\H/Γ. Here H is a finite dimensional Lie group, J ⊂ H its closed Lie subgroup and Γ ⊂ H is a discrete subgroup which acts freely and properly discontinuously on J\H. See [Gol]. In the last thirty years there was a lot of activity in the case where J is noncompact (the nonclassical