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The solution of the equation AX+BX*=0

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URI: https://hdl.handle.net/10016/22087
ISSN: 0308-1087
DOI: 10.1080/03081087.2012.750656
UXXI: AR/0000014275
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solution_LMA_2013_ps.pdf (466.59 KB)
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2013-12-01
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Taylor & Francis
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Abstract
We 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.
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Matrix equations, Matrix pencils, Kronecker canonical form, Transpose, Conjugate transpose Sylvester equation
Bibliographic citation
Linear and Multilinear Algebra 61 (2013) 12, pp.1605-1628
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