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On Hermitian positive definite solution of the matrix equation $X-\sum _{i=1}^mA_i^*X^r A_i = Q$. (English) Zbl 1170.15005
It is proved that the nonlinear matrix equation $X-\sum _{i=1}^mA_i^*X^r A_i = Q(-1\leq r < 0$ or $0< r<1)$ always has a unique Hermitian positive definite solution. Some bounds of the unique Hermitian positive definite solution are also given.

MSC:
15A24Matrix equations and identities
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References:
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