Abstract
Let A, B be any two positive definite \(n\times n\) matrices and Y be any \(n\times n\) matrix. We aim to study the precised estimates of the eigenvalues of \(M_Y(A,B)=\left[ \begin{array}{cc} A &{}\quad A^{\frac{1}{2}}YB^{\frac{1}{2}} \\ B^{\frac{1}{2}}Y^{\star }A^{\frac{1}{2}} &{}\quad B \end{array}\right] ,\) with different choices of Y as contractive, expansive or unitary matrix respectively. As applications, we also discuss the block matrices involving several means of the matrices as their entries.
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Kapil, Y., Rani, A. & Singh, M. Study of Eigenvalues of Some Matrices via Dilations. Results Math 78, 222 (2023). https://doi.org/10.1007/s00025-023-01981-9
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DOI: https://doi.org/10.1007/s00025-023-01981-9