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The Frisch scheme in algebraic and dynamic identification problems

Roberto P. Guidorzi, Roberto Diversi, Umberto Soverini (2008)

Kybernetika

This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension...

The higher rank numerical range of nonnegative matrices

Aikaterini Aretaki, Ioannis Maroulas (2013)

Open Mathematics

In this article the rank-k numerical range ∧k (A) of an entrywise nonnegative matrix A is investigated. Extending the notion of elements of maximum modulus in ∧k (A), we examine their location on the complex plane. Further, an application of this theory to ∧k (L(λ)) of a Perron polynomial L(λ) is elaborated via its companion matrix C L.

The k-Fibonacci matrix and the Pascal matrix

Sergio Falcon (2011)

Open Mathematics

We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.

The local relaxation flow approach to universality of the local statistics for random matrices

László Erdős, Benjamin Schlein, Horng-Tzer Yau, Jun Yin (2012)

Annales de l'I.H.P. Probabilités et statistiques

We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues {xj}j=1N are close to their classical location {γj}j=1N determined by the limiting density of eigenvalues. Under...

The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree

Rosário Fernandes (2015)

Special Matrices

The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M1, was understood fully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra 46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree, we focus upon M2, the maximum value of the sum of the two largest multiplicities when the largest multiplicity is M1. Upper and lower bounds are given for M2. Using a combinatorial...

The minimum, diagonal element of a positive matrix

M. Smyth, T. West (1998)

Studia Mathematica

Properties of the minimum diagonal element of a positive matrix are exploited to obtain new bounds on the eigenvalues thus exhibiting a spectral bias along the positive real axis familiar in Perron-Frobenius theory.

The P 0 -matrix completion problem.

Choi, Ji Young, DeAlba, Luz Maria, Hogben, Leslie, Maxwell, Mandi S., Wangsness, Amy (2002)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The primitive Boolean matrices with the second largest scrambling index by Boolean rank

Yan Ling Shao, Yubin Gao (2014)

Czechoslovak Mathematical Journal

The scrambling index of an n × n primitive Boolean matrix A is the smallest positive integer k such that A k ( A T ) k = J , where A T denotes the transpose of A and J denotes the n × n all ones matrix. For an m × n Boolean matrix M , its Boolean rank b ( M ) is the smallest positive integer b such that M = A B for some m × b Boolean matrix A and b × n Boolean matrix B . In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an n × n primitive matrix M in terms of its Boolean rank b ( M ) , and they also characterized all primitive...

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