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Positive definite solution of the matrix equation(oldsymbol {X=Q+A^{H}(Iotimes X-C)^{delta}A})

✍ Scribed by Guozhu Yao; Anping Liao; Xuefeng Duan


Publisher
Springer US
Year
2010
Tongue
English
Weight
305 KB
Volume
56
Category
Article
ISSN
1017-1398

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The Hermitian positive definite solutions of the matrix equation X + A \* X -2 A = I are studied. A necessary and sufficient condition for existence of solutions is given in case A is normal. The basic fixed point iterations for the equation in case A is nonnormal with A are discussed in some detai

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Consider the nonlinear matrix equation where Q is an n Γ— n Hermitian positive definite matrix, C is an mn Γ— mn Hermitian positive semidefinite matrix, A is an mn Γ— n matrix, and X is the m Γ— m block diagonal matrix defined by X = diag(X, X, . . . , X), in which X is an n Γ— n matrix. This matrix equ