Fischer determinantal inequalities and Highamʼs Conjecture
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 کاملDeterminantal Inequalities for Block Triangular Matrices
This paper presents some results that complement (2). We believe our results are of new pattern concerning determinantal inequalities. Let us fix some notation. The matrices considered here have entries from the field of complex numbers. X ′,X ,X∗ stand for transpose, (entrywise)conjugate, conjugate transpose of X , respectively. For two n -square Hermitian matrices X ,Y , we write X > Y to mea...
متن کاملChvátal's conjecture and correlation inequalities
Chvátal’s conjecture in extremal combinatorics asserts that for any decreasing family F of subsets of a finite set S, there is a largest intersecting subfamily of F consisting of all members of F that include a particular x ∈ S. In this paper we reformulate the conjecture in terms of influences of variables on Boolean functions and correlation inequalities, and study special cases and variants ...
متن کاملSome New Results on Determinantal Inequalities and Applications
Some new upper and lower bounds on determinants are presented for diagonally dominant matrices and general H-matrices by using different methods. These bounds are some improvements of results given by Ostrowski 1952 and 1937 , Price 1951 , Wang and Zhang 2002 , Huang and Liu 2005 , and so forth. In addition, these bounds are also used to localize some numerical characters e.g., the minimum eige...
متن کاملIsoperimetric Inequalities and the Friedlander–milnor Conjecture
We prove that Friedlander’s generalized isomorphism conjecture on the cohomology of algebraic groups, and hence Milnor’s conjecture on the cohomology of the complex algebraic Lie group G(C) made discrete, are equivalent to the existence of an isoperimetric inequality in the homological bar complex of G(F ), where F is the algebraic closure of a finite field.
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: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.08.031