Results 101 to 110 of about 10,056 (177)
On weakly unitarily invariant norm and the Aluthge transformation
Linear Algebra and its Applications, 2003 The main result: \(|||f(P^\lambda UP^{1-\lambda})|||\leq \max\{|||f(T)|||, |||U^* f(T)U+ f(0)(I- U^* U)|||\}\), where \(T\in B(H)\) is a bounded linear operator on a Hilbert space \(H\), \(f\) is a polynomial, and \(|||\cdot|||\) is a seminorm on \(H\) which satisfies the following two conditions: a) \(\exists\gamma> 0\) such that \(|||X|||\leq \gamma\|
openaire +2 more sources
, 2001 A result of R. Mathias and Horn [cf. Linear Algebra Appl. 142 (1990) 63] on the representation of the unitarily invariant norm is extended in the context of Eaton triples and of real semisimple Lie algebras. The representation is related to a function ∥·∥
Hill, William C. +3 more
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Environment-Assisted Shortcuts to Adiabaticity. [PDF]
Entropy (Basel), 2021 Touil A, Deffner S.
europepmc +1 more source
Cauchy-Schwarz inequalities associated with positive semidefinite matrices
, 1990 Using a quasilinear representation for unitarily invariant norms, we prove a basic inequality: Let A=LXX∗M be positive semidefinite, where X∈Mm,n. Then |||X|p||2⩽‖Lp‖ ‖Mp‖ for all p>0 and all unitarily invariant norms ‖·‖.
Horn, Roger A., Mathias, Roy
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Pinchings and norms of scaled triangular matrices
, 2002 Suppose U is an upper-triangular matrix, and D a nonsingular diagonal matrix whose diagonal entries appear in non- descending order of magnitude down the diagonal. It is proved that ||D-1UD||≥||U|| for any matrix norm that is reduced by a pinching.
Li, Ren-Cang +2 more
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The convex analysis of unitarily invariant matrix functions
, 1995 A fundamental result of von Neumann's identies unitarily invariant matrix norms as symmetric gauge functions of the singular values. Identifying the subdierential of such a norm is important in matrix approximation algorithms, and in studying the ...
A. S. Lewis
core
On norms of principal submatrices
, 2021 Let a norm on the set Mn of real or complex n-by-n matrices be given. We investigate the question of finding the largest constants αn and βn such that for each A∈Mn the average of the norms of its (n−1)-by-(n−1) principal submatrices is at least αn times
Rump, Siegfried M. +2 more
core
Some norm inequalities for matrix means
, 2016 Inequalities for unitarily invariant norms of power means of positive definite matrices are ...
Bhatia, Rajendra +2 more
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Convergence Rates for the Quantum Central Limit Theorem. [PDF]
Commun Math Phys, 2021 Becker S, Datta N, Lami L, Rouzé C.
europepmc +1 more source
Lower bounds for the low-rank matrix approximation. [PDF]
J Inequal Appl, 2017 Li J, Liu Z, Li G.
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