Results 11 to 20 of about 486 (86)
Inequalities related to Bourin and Heinz means with a complex parameter [PDF]
, 2015 A conjecture posed by S. Hayajneh and F. Kittaneh claims that given A, B positive matrices, 0≤t≤1, and any unitarily invariant norm the following inequality holds{triple vertical-rule fence}AtB1-t+BtA1-t{triple vertical-rule fence}≤{triple vertical-rule ...
Bottazzi, Tamara Paula +3 more
core +3 more sources
Numerical radius and zero pattern of matrices [PDF]
, 2007 We give tight upper bounds on the numerical range of square matrices in terms of their Frobenius (Euclidian) norm and a combinatorial parameter similar to the clique number of graphs.
Bollobás +7 more
core +3 more sources
On a decomposition lemma for positive semi-definite block-matrices [PDF]
, 2012 This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite ...
Bourin, Jean-Christophe +2 more
core +2 more sources
On trace inequalities and their applications to noncommutative communication theory [PDF]
, 2004 Certain trace inequalities related to matrix logarithm are shown. These results enable us to give a partial answer of the open problem conjectured by A.S.Holevo. That is, concavity of the auxiliary function which appears in the random coding exponent
Furuichi, Shigeru +2 more
core +4 more sources
Cauchy′s interlace theorem and lower bounds for the spectral radius
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 8, Page 563-566, 2000., 2000 We present a short and simple proof of the well‐known Cauchy interlace theorem. We use the theorem to improve some lower bound estimates for the spectral radius of a real symmetric matrix.
A. McD. Mercer, Peter R. Mercer
wiley +1 more source
Some Inequalities Related to the Seysen Measure of a Lattice [PDF]
, 2009 Given a lattice $L$, a basis $B$ of $L$ together with its dual $B^*$, the orthogonality measure $S(B)=\sum_i ||b_i||^2 ||b_i^*||^2$ of $B$ was introduced by M. Seysen in 1993.
Maze, Gerard
core +3 more sources
Exclusion sets in the S-type eigenvalue localization sets for tensors
Open Mathematics, 2019 In this paper, we break the index set N into disjoint subsets S and its complement, and propose two S-type exclusion sets that all the eigenvalues do not belong to them.
Zhang Yuan, Zhang Ying, Wang Gang
doaj +1 more source
A lower bound for the smallest singular value
, 2012 In this paper, we obtain a lower bound for the smallest singular value of nonsingular matrices which is better than the bound presented by Yu and Gu [Linear Algebra Appl. 252(1997)25-38].
L. Zou
semanticscholar +1 more source
Inequalities for certain powers of several positive definite matrices
Mathematical Inequalities & Applications, 2019 Let Ai, i = 1, ...,m, and X be n×n matrices such that each Ai is positive definite with 0 < ai sn (Ai) and X is Hermitian. Then it is shown that ∣∣∣∣ ∣∣∣∣ ∣∣∣∣ ( m ∑ i=1 A am+1−i i ) X +X ( m ∑ i=1 Ai m+1−i ∣∣∣∣ ∣∣∣∣ ∣∣∣∣ m(1+ l2) |||X ||| , for every ...
Fadi Alrimawi
semanticscholar +1 more source
Some inequalities involving operator monotone functions and operator means
, 2016 In this paper we show that if f : [0,∞) → [0,∞) is an operator monotone function and A,B are positive operators such that 0 < pA B qA , then for all α ∈ [0,1] f (A) α f (B) max{S(p),S(q)} f (A αB), where S(t) is the so called Specht’s ratio, and α is α ...
M. Ghaemi, V. Kaleibary
semanticscholar +1 more source