Quadratische Formen und die Artin-Schreiersche Theorie der formal reellen Körper
Quadratische Identitäten bei Polygonen.
Quadratische Räume mit zwei Unterräumen.
Quadratische Räume unendlicher Dimension und partielle Isomorphismen.
Quadratische Semi-Ordnungen und Quadratische Formen.
Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices
This paper investigates hyperbolic polynomials with quasianalytic coefficients. Our main purpose is to prove factorization theorems for such polynomials, and next to generalize the results of K. Kurdyka and L. Paunescu about perturbation of analytic families of symmetric matrices to the quasianalytic setting.
Quelques remarques sur les résultats de Tutte concernant le problème de Ulam
Quelques résultats de finitude en théorie des invariants
Raffinement de la borne spectrale d'un faisceau de matrices
Random matrices, non-colliding processes and queues
Range symmetric matrices in Minkowski space.
Ranges of Sylvester maps and a minimal rank problem.
Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix.
Rank and perimeter preserver of rank-1 matrices over max algebra
For a rank-1 matrix over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or with some monomial matrices U and V.
Rank decomposition in zero pattern matrix algebras
For a block upper triangular matrix, a necessary and sufficient condition has been given to let it be the sum of block upper rectangular matrices satisfying certain rank constraints; see H. Bart, A. P. M. Wagelmans (2000). The proof involves elements from integer programming and employs Farkas' lemma. The algebra of block upper triangular matrices can be viewed as a matrix algebra determined by a pattern of zeros. The present note is concerned with the question whether the decomposition result referred...
Rank of matrices and the Pexider equation.
Rank of tensors of -out-of- functions: An application in probabilistic inference
Bayesian networks are a popular model for reasoning under uncertainty. We study the problem of efficient probabilistic inference with these models when some of the conditional probability tables represent deterministic or noisy -out-of- functions. These tables appear naturally in real-world applications when we observe a state of a variable that depends on its parents via an addition or noisy addition relation. We provide a lower bound of the rank and an upper bound for the symmetric border rank...
Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems
As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.
Ranked solutions of the matric equation .
Rank-one LMI approach to robust stability of polynomial matrices
Necessary and sufficient conditions are formulated for checking robust stability of an uncertain polynomial matrix. Various stability regions and uncertainty models are handled in a unified way. The conditions, stemming from a general optimization methodology similar to the one used in -analysis, are expressed as a rank-one LMI, a non-convex problem frequently arising in robust control. Convex relaxations of the problem yield tractable sufficient LMI conditions for robust stability of uncertain...