منابع مشابه
A Log-Det Inequality for Random Matrices
We prove a new inequality for the expectation E [log det (WQ+ I)], where Q is a nonnegative definite matrix and W is a diagonal random matrix with identically distributed nonnegative diagonal entries. A sharp lower bound is obtained by substituting Q by the diagonal matrix of its eigenvalues Γ. Conversely, if this inequality holds for all Q and Γ, then the diagonal entries of W are necessarily ...
متن کاملOn Orthogonal Matrices Maximizing the 1-norm
For U ∈ O(N) we have ||U ||1 ≤ N √ N , with equality if and only if U = H/ √ N , with H Hadamard matrix. Motivated by this remark, we discuss in this paper the algebraic and analytic aspects of the computation of the maximum of the 1-norm on O(N). The main problem is to compute the k-th moment of the 1-norm, with k →∞, and we present a number of general comments in this direction. Introduction ...
متن کاملDiagonal Norm Hermitian Matrices
If v is a norm on en, let H(v) denote the set of all norm-Hermitians in e nn. Let S be a subset of the set of real diagonal matrices D. Then there exists a norm v such that S = H(v) (or S = H(v) n D) if and only if S contains the identity and S is a subspace of D with a basis consisting of rational vectors. As a corollary, it is shown that, for a diagonable matrix h with distinct eigenvalues .1...
متن کاملFuzzy Topology Generated by Fuzzy Norm
In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...
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: International Journal of Pure and Apllied Mathematics
سال: 2014
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v92i1.1