Ferreyra, DE.; Latanzi, M.; Levis, F.; Thome, N. (2019). Parametrized solutions X of the system AXA = AEA and A^k EAX = XAEA^k for a matrix A having index k. The Electronic Journal of Linear Algebra. 35:503-510. https://doi.org/10.13001/1081-3810.4051
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/140505
Title:
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Parametrized solutions X of the system AXA = AEA and A^k EAX = XAEA^k for a matrix A having index k
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Author:
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Ferreyra, David Eduardo
Latanzi, Marina
Levis, Fabian
Thome, Néstor
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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[EN] Let A and E be n x n given complex matrices. This paper provides a necessary and sufficient condition for the solvability to the matrix equation system given by AXA = AEA and A(k) EAX = XAEA(k) , for k being the index ...[+]
[EN] Let A and E be n x n given complex matrices. This paper provides a necessary and sufficient condition for the solvability to the matrix equation system given by AXA = AEA and A(k) EAX = XAEA(k) , for k being the index of A. In addition, its general solution is derived in terms of a G-Drazin inverse of A. As consequences, new representations are obtained for the set of all G-Drazin inverses; some interesting applications are also derived to show the importance of the obtained formulas.
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Subjects:
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Matrix equations
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Index
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G-Drazin inverses
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Generalized inverses
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Copyrigths:
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Reserva de todos los derechos
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Source:
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The Electronic Journal of Linear Algebra. (issn:
1081-3810
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DOI:
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10.13001/1081-3810.4051
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Publisher:
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University of Wyoming Libraries
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Publisher version:
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https://doi.org/10.13001/1081-3810.4051
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Project ID:
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info:eu-repo/grantAgreement/UNLP//155%2F14/
info:eu-repo/grantAgreement/CONICET//PIP 11220150100433CO/
info:eu-repo/grantAgreement/UNRC//PPI 18%2FC472/
info:eu-repo/grantAgreement/UNS//UNS%2F24%2FL108/
info:eu-repo/grantAgreement/AEI//MTM2017-90682-REDT/ES/RED TEMATICA DE ALGEBRA LINEAL, ANALISIS MATRICIAL Y APLICACIONES/
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Thanks:
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Partially supported by Universidad Nacional de Rio Cuarto (grant PPI 18/C472) and CONICET (grant PIP 112-201501-00433CO).
Partially supported by Universidad Nacional de La Pampa, Facultad de Ingenieria (grant Resol. ...[+]
Partially supported by Universidad Nacional de Rio Cuarto (grant PPI 18/C472) and CONICET (grant PIP 112-201501-00433CO).
Partially supported by Universidad Nacional de La Pampa, Facultad de Ingenieria (grant Resol. Nro. 155/14).
Partially supported by Ministerio de Economia, Industria y Competitividad of Spain (grant Red de Excelencia MTM2017-90682-REDT) and by Universidad Nacional del Sur of Argentina (grant 24/L108).
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Type:
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Artículo
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