### Some considerations of matrix equations using the concept of reproductivity

Branko Malešević, Biljana Radičić (2012)

Kragujevac Journal of Mathematics

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Branko Malešević, Biljana Radičić (2012)

Kragujevac Journal of Mathematics

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Enrique Navarro, Rafael Company, Lucas Jódar (1993)

Applicationes Mathematicae

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In this paper we consider Bessel equations of the type ${t}^{2}{X}^{\left(2\right)}\left(t\right)+t{X}^{\left(1\right)}\left(t\right)+({t}^{2}I-{A}^{2})X\left(t\right)=0$, where A is an n$\times $n complex matrix and X(t) is an n$\times $m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.

Neuwirth, Erich (2002)

Séminaire Lotharingien de Combinatoire [electronic only]

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Zhang, X. (2004)

Acta Mathematica Universitatis Comenianae. New Series

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Gildea, Joe (2008)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Sakhnovich, Alexander (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Krzysztof Moszyński (1995)

Applicationes Mathematicae

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Murty, M.S.N., Anjaneyulu, D., Kumar, G.Suresh (2011)

The Journal of Nonlinear Sciences and its Applications

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Lomidze, I. (1994)

Georgian Mathematical Journal

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Karol Pąk (2008)

Formalized Mathematics

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In this paper I present the Kronecker-Capelli theorem which states that a system of linear equations has a solution if and only if the rank of its coefficient matrix is equal to the rank of its augmented matrix.MML identifier: MATRIX15, version: 7.8.09 4.97.1001

Peradze, J. (2007)

Bulletin of TICMI

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A. R. Moghaddamfar, S. M. H. Pooya, S. Navid Salehy, S. Nima Salehy (2012)

Matematički Vesnik

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