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On Additive Decomposition of the Hermitian Solution of the Matrix Equation AXA* = B

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Abstract

The decomposition of a Hermitian solution of the linear matrix equation AXA* = B into the sum of Hermitian solutions of other two linear matrix equations \({A_{1}X_{1}A^{*}_{1} = B_{1}}\) and \({A_{2}X_{2}A^*_{2} = B_{2}}\) are approached. As applications, the additive decomposition of Hermitian generalized inverse C − = A − + B − for three Hermitian matrices A, B and C is also considered.

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  1. China Economics and Management Academy, Central University of Finance and Economics, Beijing, 100081, China

    Yongge Tian

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  1. Yongge Tian
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Tian, Y. On Additive Decomposition of the Hermitian Solution of the Matrix Equation AXA* = B . Mediterr. J. Math. 9, 47–60 (2012). https://doi.org/10.1007/s00009-010-0110-8

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  • DOI: https://doi.org/10.1007/s00009-010-0110-8

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