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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 Gerschgorin discs under unitary similarity

Anna Zalewska-Mitura, Jaroslav Zemánek (1997)

Banach Center Publications

The intersection of the Gerschgorin regions over the unitary similarity orbit of a given matrix is studied. It reduces to the spectrum in some cases: for instance, if the matrix satisfies a quadratic equation, and also for matrices having "large" singular values or diagonal entries. This leads to a number of open questions.

The group of commutativity preserving maps on strictly upper triangular matrices

Deng Yin Wang, Min Zhu, Jianling Rou (2014)

Czechoslovak Mathematical Journal

Let 𝒩 = N n ( R ) be the algebra of all n × n strictly upper triangular matrices over a unital commutative ring R . A map ϕ on 𝒩 is called preserving commutativity in both directions if x y = y x ⇔ ϕ ( x ) ϕ ( y ) = ϕ ( y ) ϕ ( x ) . In this paper, we prove that each invertible linear map on 𝒩 preserving commutativity in both directions is exactly a quasi-automorphism of 𝒩 , and a quasi-automorphism of 𝒩 can be decomposed into the product of several standard maps, which extains the main result of Y. Cao, Z. Chen and C. Huang (2002) from fields to rings.

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 inertia set of nonnegative symmetric sign pattern with zero diagonal

Yubin Gao, Yan Ling Shao (2003)

Czechoslovak Mathematical Journal

The inertia set of a symmetric sign pattern A is the set i ( A ) = { i ( B ) ∣ B = B T ∈ Q ( A ) } , where i ( B ) denotes the inertia of real symmetric matrix B , and Q ( A ) denotes the sign pattern class of A . In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern A in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns A with zero diagonal that require...

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