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Displaying similar documents to “A note on the general Hermitian solution to A X A * = B .”

Inertias and ranks of some Hermitian matrix functions with applications

Xiang Zhang, Qing-Wen Wang, Xin Liu (2012)

Open Mathematics

Similarity:

Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively....

Perturbation theorems for Hermitian elements in Banach algebras

Rajendra Bhatia, Driss Drissi (1999)

Studia Mathematica

Similarity:

Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.