POSITIVE MATRICES WITH PRESCRIBED SINGULAR VALUES
نویسندگان
چکیده
منابع مشابه
Nonnegative matrices with prescribed extremal singular values
We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. In particular, given 2n−1 real numbers σ ( j) 1 and σ ( j) j , j = 1, . . . , n, we construct an n×n nonnegative bidiagonal matrix B and an n×n nonnegative semi-bordered diagonal matrix C , such that σ ( j) 1 and σ ( j) j are, respectively, the minimal and the maximal singular values of certai...
متن کاملOn singular values of partially prescribed matrices
In this paper we study singular values of a matrix whose one entry varies while all other entries are prescribed. In particular, we find the possible pth singular value of such a matrix, and we define explicitly the unknown entry such that the completed matrix has the minimal possible pth singular value. This in turn determines possible pth singular value of a matrix under rank one perturbation...
متن کاملConstruction of matrices with prescribed singular values and eigenvalues
Two issues concerning the construction of square matrices with prescribed singular values and eigenvalues are addressed. First, a necessary and sufficient condition for the existence of an n × n complex matrix with n given nonnegative numbers as singular values and m(≤ n) given complex numbers to be m of the eigenvalues is determined. This extends the classical result of Weyl and Horn treating ...
متن کاملOn Constructing Matrices with Prescribed Singular Values and Diagonal Elements
Similar to the well known Schur Horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix the Sing Thompson theorem characterizes the relationship between the diagonal en tries and the singular values of an arbitrary matrix It is noted in this paper that based on the induction principle such a matrix can be constructed numerically by...
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 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: Proyecciones (Antofagasta)
سال: 2008
ISSN: 0716-0917
DOI: 10.4067/s0716-09172008000300005