Matrix Inequalities

By Xingzhi Zhan. 2002

356 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8a772d89b7b19bec231e35871fbe4cccfd1e121a

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In Computational Theory and Mathematics

In Electrical and Electronic Engineering

In Geometry and Topology

Citations in the corpus

The matrix arithmetic-geometric mean inequality revisited (2008, background): “Zhan [38] showed that the Level 3 inequality (3.5) can be enhanced to a Level 2 version, sj (A − B) sj (A ⊕ B), 1 j n (3.6) and further, this statement is equivalent to the AGMI (3.1).”
Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (2005, unknown): “(Proof: See [23,625].”
Introduction to Matrix Analysis and Applications (2014, background): “Falikman, it is also included in the book [81].”
Variance bounds, with an application to norm bounds for commutators (2009, methodology): “For the Cartesian modulus this is no longer true, but we do have the following inequalities for Schatten p-norms obtained by Bhatia and Kittaneh ([15], eqns (3.38) and (3.39)): for p ≥ 2, || |X|C ||p ≤ ||X||p ≤ 21/2−1/p|| |X|C ||p, (24) while the reversed inequalities hold for 1 ≤ p ≤ 2.”
A parameterization of positive definite matrices in terms of partial correlation vines (2003, methodology): “In particular, we present effective procedures for deciding whether a partially specified matrix can be extended to a positive definite matrix for certain non-chordal graphs [3,5,6,9,10].”
A note on operator inequalities of Tsallis relative operator entropy (2005, unknown): “From the deﬁnition, we easily ﬁnd that lim λ → 0 T λ (A | B) = S(A | B), since ln λ (x) ≡ x λ − 1 λ uniformly converges to log x for x (cid:2) 0 by Dini’s theorem.”
Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph (2009, background): “3 (Schatten bound [29], proof of Theorem 3.”