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On relations among solutions of the Hermitian matrix equation $AXA^{*} = B$ and its three small equations

2014
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Annals of Functional Analysis
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Assume that the linear matrix equation AXA * = B = B * has a Hermitian solution and is partitioned as . We study in this paper relations among the Hermitian solutions of the equation and the three small-size matrix equations A 1 X 1 A * 1 = B 11 , A 1 X 2 A * 2 = B 12 and A 2 X 3 A * 2 = B 22 . In particular, we establish closed-form formulas for calculating the maximal and minimal ranks and inertias of X − X 1 − X 2 − X * 2 − X 3 , and use the formulas to derive necessary and sufficient

doi:10.15352/afa/1396833500
fatcat:fyj5eg7aqba5dclwtfrknxbbzm