منابع مشابه
Ela Singular Values of Tournament Matrices
Upper and lower bounds on both the largest and smallest singular values of a tournament matrix M of order n are obtained. For most values of n, the matrices M for which equality holds are characterized.
متن کاملSingular values of convex functions of matrices
Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$ are nonzero matrices and each $X_{i}$ is positive semidefinite. It is shown that if $f$ is a nonnegative increasing convex function on $left[ 0,infty right) $ satisfying $fleft( 0right) =0 $, then $$2s_{j}left( fleft( fra...
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 کاملAccurate Singular Values of Bidiagonal Matrices
2 has nonzero entries only on its diagonal and first superdiagonal ) Compute orthogonal matrices P and Q such that Σ = P BQ is diagonal and nonnegat i 2 2 2 T 2 ive. The diagonal entries σ of Σ are the singular values of A . We will take them to be sorted in decreasing order: σ ≥ σ . The columns of Q= Q Q are the right singular vec i i + 1 1 2 t 1 2 ors, and the columns of P= P P are the left s...
متن کاملOn the singular values of random matrices
We present an approach that allows one to bound the largest and smallest singular values of an N × n random matrix with iid rows, distributed according to a measure on R that is supported in a relatively small ball and linear functionals are uniformly bounded in Lp for some p > 8, in a quantitative (non-asymptotic) fashion. Among the outcomes of this approach are optimal estimates of 1±c √ n/N ...
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: The Electronic Journal of Linear Algebra
سال: 1999
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1030