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Inequalities for Unitarily Invariant Norms
SIAM Journal on Matrix Analysis and Applications, 1998Let \(A,B,X\) be complex matrices with \(A,B\) positive semidefinite. The author proves the following generalization of the arithmetic-mean inequality due to \textit{R. Bhatia} and \textit{C. Davis} [ibid. 14, No. 1, 132-136 (1993; Zbl 0767.15012]: \[ (2+t)\| A^rXB^{2-r}+A^{2-r}XB^r\| \leq 2\| A^2X+tAXB+XB^2\| \] for arbitrary unitarily invariant norm \
Xingzhi Zhan
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Unitarily invariant norms on dual quaternion matrices
Pacific Journal of OptimizationSummary: Dual quaternion matrices have recently received significant attention in research. In this paper, we primarily investigate unitarily invariant norms of dual quaternion matrices. We first introduce symmetric gauge function on dual numbers and establish a one-to-one correspondence between unitarily invariant norms of dual quaternion matrices and
Chen, Sheng, Hu, Haofei
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Interpolating inequalities for unitarily invariant norms of matrices
Advances in Operator TheoryzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Omar Hirzallah +2 more
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SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
Quarterly Journal of Mathematics, 1960Mirsky L, L Mirsky
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Unitarily Invariant Operator Norms
Canadian Journal of Mathematics, 19831.1. Over the past 15 years there has grown up quite an extensive theory of operator norms related to the numerical radius1of a Hilbert space operator T. Among the many interesting developments, we may mention:(a) C. Berger's proof of the “power inequality”2(b) R. Bouldin's result that3for any isometry V commuting with T;(c) the unification by B.
Fong, C.-K., Holbrook, J. A. R.
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A note on unitarily invariant matrix norms
Linear Algebra and its Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Wenxuan, Li, Chi-Kwong, Li, Yuqiao
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Unitarily invariant norm submultiplicativity
Linear and Multilinear Algebra, 1992In this paper, we view rules for multiplying matrices (such as the Hadamard product, usual product and Kronecker product) as combinatorial objects. Our purpose is to determine conditions on these objects that imply submultiplicativity with respect to the spectral norm and certain of the unitarily invariant norms.
Charles R. Johnson, Peter Nylen
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Unitarily Invariant Norms and Rearrangement
2019In the next chapter, we will discuss some operator norm inequalities for matrix monotone functions and also some functions which are functional inverses of matrix monotone functions.
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