Singular values, doubly stochastic matrices, and applications

  title={Singular values, doubly stochastic matrices, and applications},
  author={Ludwig Elsner and Shmuel Friedland},
  journal={Linear Algebra and its Applications},
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
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
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
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...
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


A proof of a generalized van der Waerden conjecture on permanents
Let A be an n × n matrix. Denote by σ k (A) the sum of all subpermanents of A of order k. Then on the set of doubly stochastic matrices σ k attains its minimum only on the matrix .
The Complexity of Computing the Permanent
  • L. Valiant
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1979
On perturbations of matrix pencils with real spectra
Perturbation bounds for the generalized eigenvalue problem of a diagonalizable matrix pencil A -AB with real spectrum are developed. It is shown how the chordal distances between the generalized
The Maximum Number of Disjoint Permutations Contained in a Matrix of Zeros and Ones
A well-known consequence of the König theorem on maximum matchings and minimum covers in bipartite graphs (5) or of the P. Hall theorem on systems of distinct representatives for sets (4) asserts
Every 7-regular digraph contains an even cycle
The even cycle problem for directed graphs
If each arc in a strongly connected directed graph of minimum in- degree and outdegree at least 3 is assigned a weight 0 or 1, then the resulting weighted directed graph has a directed cycle of even
Additive decomposition of nonnegative matrices with applications to permanents and scalingt
Let U1 and U2 be compact subsets of m × n nonnegative matrices with prescribed row sums and column sums. Given A in U2 , we study the quantity and the matrices B in U1 that satisfy A−μ(U1;A)B is