Singular Values, Eigenvalues and Diagonal Elements Of The Commutator Of 2x2 Rank One Matrices
نویسندگان
چکیده
منابع مشابه
Matrix Reconstruction with Prescribed Diagonal Elements, Eigenvalues, and Singular Values
DIAGONAL ELEMENTS, EIGENVALUES, AND SINGULAR VALUES DRAFT AS OF April 30, 2013 SHENG-JHIH WU AND MOODY T. CHU Abstract. Diagonal entries and eigenvalues of a Hermitian matrix, diagonal entries and singular values of a general matrix, and eigenvalues and singular values of a general matrix satisfy necessarily some majorization relationships which turn out also to be sufficient conditions. The in...
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 کاملAccurate computation of singular values and eigenvalues of symmetric matrices ∗
We give the review of recent results in relative perturbation theory for eigenvalue and singular value problems and highly accurate algorithms which compute eigenvalues and singular values to the highest possible relative accuracy.
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 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: 2020
ISSN: 1081-3810
DOI: 10.13001/ela.2020.4955