On a criterion of Yakubovich type for the absolute stability of nonautonomous control processes.
An inclusion region for the field of values of a doubly stochastic matrix based on its graph. (Short Communication).
An inclusion region for the field of values of a doubly stochastic matrix based on its graph.
A result for the 'other' variable of Ramanujan's sum.
Reminiscences on Miroslav Fiedler
The combinatorially symmetric -matrix completion problem.
Totally positive completions for monotonically labeled block clique graphs.
Constructing copositive matrices from interior matrices.
Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix.
Conditions for a totally positive completion in the case of a symmetrically placed cycle.
Local and global null controllability of time varying linear control systems
Local and global null controllability of time varying linear control systems
For linear control systems with coefficients determined by a dynamical system null controllability is discussed. If uniform local null controllability holds, and if the Lyapounov exponents of the homogeneous equation are all non-positive, then the system is globally null controllable for almost all paths of the dynamical system. Even if some Lyapounov exponents are positive, an irreducibility assumption implies that, for a dense set of paths, the system is globally null controllable.
Surprising Determinantal Inequality for Real Matrices.
The classification of edges and the change in multiplicity of an eigenvalue of a real symmetric matrix resulting from the change in an edge value
We take as given a real symmetric matrix A, whose graph is a tree T, and the eigenvalues of A, with their multiplicities. Each edge of T may then be classified in one of four categories, based upon the change in multiplicity of a particular eigenvalue, when the edge is removed (i.e. the corresponding entry of A is replaced by 0).We show a necessary and suficient condition for each possible classification of an edge. A special relationship is observed among 2-Parter edges, Parter edges and singly...
Sufficient conditions to be exceptional
A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A is exceptional. We also show that the only 5-by-5 exceptional matrix with a hollow nonnegative inverse is the Horn matrix (up to positive diagonal congruence and permutation similarity).
Patterns of commutativity: the commutant of the full pattern.
Matrices totally positive relative to a tree.
The general totally positive matrix completion problem with few unspecified entries.
Inequalities involving immanants and diagonal products for H-matrices and positive definite matrices
Absolutely flat idempotents.
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