Norm inequalities for matrix geometric means of positive definite matrices |
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| Authors: | Jun Ichi Fujii Takeaki Yamazaki |
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| Institution: | 1. Department of Art and Sciences (Information Science), Osaka Kyoiku University, Osaka, Japan.;2. Department of Electrical, Electronic and Computer Engineering, Toyo University, Saitama, Japan. |
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| Abstract: | We obtain eigenvalue inequalities for matrix geometric means of positive definite matrices. This implies matrix norm inequalities for unitarily invariant norms, which are considered as complementary to a series of norm inequalities among geometric means. We give complements of the Ando–Hiai type inequality for the Karcher mean by means of the generalized Kantorovich constant. Finally, we consider the monotonicity of the eigenvalue function for the Karcher mean. |
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| Keywords: | Karcher mean chaotic geometric mean matrix geometric mean unitarily invariant norm Kantorovich constant Ando–Hiai inequality |
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