Terán Vergara, Fernando de2015-12-112015-12-112013-12-01Linear and Multilinear Algebra 61 (2013) 12, pp.1605-16280308-1087https://hdl.handle.net/10016/22087We give a complete solution of the matrix equation AX+BX=0, where A, B ∈ C^mxn are two given matrices, X ∈ C^mxn is an unknown matrix, and denotes the transpose or the conjugate transpose. We provide a closed formula for the dimension of the solution space of the equation in terms of the Kronecker canonical form of the matrix pencil A+B, and we also provide an expression for the solution X in terms of this canonical form, together with two invertible matrices leading A+B to the canonical form by strict equivalence.application/pdfeng© 2013 Taylor & FrancisMatrix equationsMatrix pencilsKronecker canonical formTransposeConjugate transpose Sylvester equationresearch articleMatemáticas10.1080/03081087.2012.750656open access1605121628Linear and Multilinear Algebra61AR/0000014275