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Essential sign change numbers of full sign pattern matrices

Xiaofeng Chen, Wei Fang, Wei Gao, Yubin Gao, Guangming Jing, Zhongshan Li, Yanling Shao, Lihua Zhang (2016)

Special Matrices

A sign pattern (matrix) is a matrix whose entries are from the set {+, −, 0} and a sign vector is a vector whose entries are from the set {+, −, 0}. A sign pattern or sign vector is full if it does not contain any zero entries. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. The notions of essential row sign change number and essential column sign change number are introduced for full sign...

Estimation of the noncentrality matrix of a noncentral Wishart distribution with unit scale matrix. A matrix generalization of Leung's domination result.

Heinz Neudecker (2004)

SORT

The main aim is to estimate the noncentrality matrix of a noncentral Wishart distribution. The method used is Leung's but generalized to a matrix loss function. Parallelly Leung's scalar noncentral Wishart identity is generalized to become a matrix identity. The concept of Löwner partial ordering of symmetric matrices is used.

Étienne Bézout : analyse algébrique au siècle des lumières

Liliane Alfonsi (2008)

Revue d'histoire des mathématiques

Le but de cet article, à travers l’étude des travaux en analyse algébrique finie d’Étienne Bézout (1730-1783), est de mieux faire connaître ses résultats, tels qu’il les a effectivement trouvés, et de mettre en valeur aussi bien les points de vue novateurs que les méthodes originales, mis en œuvre à cet effet. L’idée de ramener le problème de l’élimination d’une ou plusieurs inconnues à l’étude d’un système d’équations du premier degré, son utilisation inhabituelle des coefficients indéterminés...

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Kostov, Vladimir (2001)

Serdica Mathematical Journal

Research partially supported by INTAS grant 97-1644We consider the variety of (p + 1)-tuples of matrices Aj (resp. Mj ) from given conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) such that A1 + . . . + A[p+1] = 0 (resp. M1 . . . M[p+1] = I). This variety is connected with the weak Deligne-Simpson problem: give necessary and sufficient conditions on the choice of the conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) so that there exist (p + 1)-tuples with trivial centralizers of matrices...

Existence and construction of two-dimensional invariant subspaces for pairs of rotations

Ernst Dieterich (2009)

Colloquium Mathematicae

By a rotation in a Euclidean space V of even dimension we mean an orthogonal linear operator on V which is an orthogonal direct sum of rotations in 2-dimensional linear subspaces of V by a common angle α ∈ [0,π]. We present a criterion for the existence of a 2-dimensional subspace of V which is invariant under a given pair of rotations, in terms of the vanishing of a determinant associated with that pair. This criterion is constructive, whenever it is satisfied. It is also used to prove that every...

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