New Version of Lin, Hartfiel, and Hong-QI Inequalities for Accretive-Dissipative Matrices
Mona Sakkijha, Shatha Hasan Β· WSEAS TRANSACTIONS ON MATHEMATICS Β· 2025
Let β³ n (β) be the algebra of all π Γ π complex matrices.For any π β β³ n (β), the real part of π is π π π = π+π * 2 and the imaginary part of π is πΌπ π = π-π * 2π .Let Ξ₯, Ζ€, and Ξ¨ β β³ n (β) be accretive-dissipative matrices such that the real parts and imaginary parts of their Cartesian decompositions are positive semidefinite.In this paper, we present and prove the following determinant inequalities., and |det(Ξ₯ + Ζ€ + Ξ¨)| + |det(Ξ¨)| β₯ 2 -n 2 (|det(Ξ₯ + Ξ¨)| + |det(Ζ€ + Ξ¨)| + (2 n -2)|det(Ξ₯)| 1 2| det(Ζ€)| 1 2 + 3(3 n-1 -2 n + 1)β|det(Ξ₯)||det(Ζ€)||det(Ξ¨)| 3 ).Moreover, numerical example is tested to these inequalities.