When powers of a matrix coincide with its Hadamard powers
Roman Drnovšek (2015)
Special Matrices
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We characterize matrices whose powers coincide with their Hadamard powers.
Roman Drnovšek (2015)
Special Matrices
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We characterize matrices whose powers coincide with their Hadamard powers.
Agrawal N. Sushama, K. Premakumari, K.C. Sivakumar (2014)
Special Matrices
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A matrix A ∈ ℝn×n is a GM-matrix if A = sI − B, where 0 < ρ(B) ≤ s and B ∈WPFn i.e., both B and Bt have ρ(B) as their eigenvalues and their corresponding eigenvector is entry wise nonnegative. In this article, we consider a generalization of a subclass of GM-matrices having a nonnegative core nilpotent decomposition and prove a characterization result for such matrices. Also, we study various notions of splitting of matrices from this new class and obtain sufficient conditions for...
Luong Dinh Tin (1978)
Acta Universitatis Carolinae. Mathematica et Physica
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Saleem Al-Ashhab (2013)
Matematički Vesnik
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Zhang, X. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Ljiljana Cvetković, Vladimir Kostić, Maja Nedović (2015)
Open Mathematics
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In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already...
Anna Zalewska-Mitura, Jaroslav Zemánek (1997)
Banach Center Publications
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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.
Miroslav Fiedler, Thomas L. Markham (1994)
Mathematica Slovaca
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Christos Kravvaritis (2014)
Special Matrices
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Determinant formulas for special binary circulant matrices are derived and a new open problem regarding the possible determinant values of these specific circulant matrices is stated. The ideas used for the proofs can be utilized to obtain more determinant formulas for other binary circulant matrices, too. The superiority of the proposed approach over the standard method for calculating the determinant of a general circulant matrix is demonstrated.