A weak majorization involving the matrices A ∘ B and AB
نویسندگان
چکیده
منابع مشابه
the investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
Weak log-majorization inequalities of singular values between normal matrices and their absolute values
This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$. Some applications to these inequalities are also given. In addi...
متن کاملWeak matrix majorization
Given X, Y ∈ Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization, X w Y if there exists a row-stochastic matrix A ∈ Rn×n such that AX = Y, and consider the relations between this concept, strong majorization ( s ) and directional majorization ( ). It is verified that s⇒ ⇒ w , but none of the reciprocal implications is true. Nevertheless, we study the i...
متن کاملweak log-majorization inequalities of singular values between normal matrices and their absolute values
this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$. some applications to these inequalities are also given. in addi...
متن کاملWeak k-majorization and polyhedra
For integers k and n with k ≤ n a vector x ∈ R is said to be weakly k-majorized by a vector q ∈ R if the sum of the r largest components of x does not exceed the sum of the r largest components of q, for r = 1, . . . , k. For a given q the set of vectors weakly k-majorized by q defines a polyhedron P (q; k). We determine the vertices of both P (q; k) and its integer hull Q(q; k). Furthermore a ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)00009-3