Several new inequalities on operator means of non-negative maps and Khatri–Rao products of positive definite matrices
نویسندگان
چکیده
منابع مشابه
Determinantal inequalities for positive definite matrices
Let Ai , i = 1, . . . ,m , be positive definite matrices with diagonal blocks A ( j) i , 16 j 6 k , where A ( j) 1 , . . . ,A ( j) m are of the same size for each j . We prove the inequality det( m ∑ i=1 A−1 i ) > det( m ∑ i=1 (A (1) i ) −1) · · ·det( m ∑ i=1 (A (k) i ) −1) and more determinantal inequalities related to positive definite matrices.
متن کاملOn the Approximation of Matrix Products and Positive Definite Matrices
In this paper, we introduce and analyze new randomized and deterministic algorithms to approximate the product of two matrices. In addition we provide what is, to the best of our knowledge, the first relative error bound for the Nyström approximation of quadratic forms. While deriving the proofs of the results, we highlight several new connections between matrix products, the Nyström extension ...
متن کاملon the comparison of keyword and semantic-context methods of learning new vocabulary meaning
the rationale behind the present study is that particular learning strategies produce more effective results when applied together. the present study tried to investigate the efficiency of the semantic-context strategy alone with a technique called, keyword method. to clarify the point, the current study seeked to find answer to the following question: are the keyword and semantic-context metho...
15 صفحه اولRiemannian metrics on positive definite matrices related to means. II
On the manifold of positive definite matrices, a Riemannian metric Kφ is associated with a positive kernel function φ on (0,∞) × (0,∞) by defining K D(H,K) = ∑ i,j φ(λi, λj) TrPiHPjK, where D is a foot point with the spectral decomposition D = ∑ i λiPi and H,K are Hermitian matrices (tangent vectors). We are concerned with the case φ(x, y) = M(x, y)θ where M(x, y) is a mean of scalars x, y > 0....
متن کاملOperator norms of words formed from positive-definite matrices
Let α1, α2, . . . , αn, β1, β2, . . . , βn be strictly positive reals with α1 +α2 + · · ·+αn = β1 + β2 + · · ·+ βn = s. In this paper, the inequality |||Aα1Bβ1Aα2 · · ·AαnBβn ||| ≤ |||AB|||s when A and B are positive-definite matrices is studied. Related questions are also studied.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of King Saud University - Science
سال: 2014
ISSN: 1018-3647
DOI: 10.1016/j.jksus.2013.05.002