Singular values, doubly stochastic matrices, and applications

@article{Elsner1995SingularVD,
  title={Singular values, doubly stochastic matrices, and applications},
  author={Ludwig Elsner and Shmuel Friedland},
  journal={Linear Algebra and its Applications},
  year={1995},
  volume={220},
  pages={161-169}
}
Bounds for the relative change of singular values of a real matrix
This paper amis to derive bounds for the relative change in the singular values of a real matrix. Both the full column rank and the full row rank cases are considered. Two numerical experiments show
Multiplicative relative perturbation bounds of eigenvalues for diagonalizable matrices
TLDR
The general bounds of multiplicative relative perturbation for diagonalizable matrices are presented, which are the improvement of recent results and are sharper than those in related literatures.
On perturbation bounds of generalized eigenvalues for diagonalizable pairs
TLDR
Two perturbation bounds of the diagonalizable pairs of generalized eigenvalues are given and these results extend the corresponding ones given by Sun in 1982.
Relative perturbation bounds for eigenpairs of diagonalizable matrices
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Some uniform relative perturbation bounds for eigenvalues and eigenspaces of diagonalizable matrices under additive and multiplicative perturbations are presented.
New upper bounds for the spectral variation of a general matrix
Let A ∈ C n × n be a normal matrix with spectrum { λ i } i = 1 n , and let A ~ = A + E ∈ C n × n be a perturbed matrix with spectrum { λ ~ i } i = 1 n . If A ~ is still normal, the celebrated Hoffm...
THE EIGENVALUE PERTURBATION BOUND FOR
TLDR
Some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices are presented, which improves some recent results.
Spectral variation bounds for diagonalisable matrices
SummaryThis note is related to an earlier paper by Bhatia, Davis, and Kittaneh [4]. For matrices similar to Hermitian, we prove an inequality complementary to the one proved in [4, Theorem 3]. We
On symplectic eigenvalues of positive definite matrices
If A is a 2n × 2n real positive definite matrix, then there exists a symplectic matrix M such that MTAM=DOOD where D = diag(d1(A), …, dn(A)) is a diagonal matrix with positive diagonal entries, which
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