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A note on constructing a symmetric matrix with specified diagonal entries and eigenvalues

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Abstract

A finite step algorithm is given such that for any two vectorsa, λ ∈R n witha majorized by λ, it computes a symmetric matrixH ∈R n x n with the elements ofa and λ as its diagonal entries and eigenvalues, respectively.

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References

  1. M. Chu.Constructing a Hermitian matrix from its diagonal entries and eigenvalues, SIAM Journal on Matrix Analysis and Applications, 16(1995), pp. 207–217.

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  2. G. H. Golub and C. F. Van Loan.Matrix Computations. Johns Hopkins University Press, Baltimore, Maryland, 2nd edition, 1989.

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  3. A. W. Marshall and I. Olkin.Inequalities: Theory of Majorization and Its Applications. Academic Press, New York, 1979.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, The Pennsylvania State University, 16802, University Park, PA

    Hongyuan Zha

  2. Center for Mathematical Sciences & Department of Applied Mathematics, Zhejiang University, 310027, Hangzhou, P. R. China

    Zhenyue Zhang

Authors
  1. Hongyuan Zha
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  2. Zhenyue Zhang
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Additional information

Supported in part by NSF grant CCR-9308399.

Supported in part by China State Major Key Project for Basic Researches.

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Zha, H., Zhang, Z. A note on constructing a symmetric matrix with specified diagonal entries and eigenvalues. Bit Numer Math 35, 448–452 (1995). https://doi.org/10.1007/BF01732616

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  • DOI: https://doi.org/10.1007/BF01732616

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