Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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AN INEQUALITY ON PERMANENTS OF HADAMARD PRODUCTS

  • Published : 2000.08.01
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Abstract

Let $A=(a_{ij}\ and\ B=(b_{ij}\ be\ n\times\ n$ complex matrices and let A$\bigcirc$B denote the Hadamard product of A and B, that is $AA\circB=(A_{ij{b_{ij})$.We conjecture a permanental analog of Oppenheim's inequality and verify it for n=2 and 3 as well as for some infinite classes of matrices.

Keywords

References

  1. Linear Algebra and Appl. v.76 An extremal property of the permanent and the determinant R.B.Bapat;V.s.Sunder
  2. Amer.Math.Monthly v.89 Is there a permanental analog to Oppenheim's inequality J.Chollet
  3. Linear Algebra and Appl. v.94 A note on the analog to Oppenheim's inequality R.J.Gregorac;I.R.Hensel
  4. Linear and Multilinear Algebra v.212 no.213 Notes on Hadamard products of matrices F.-Z.Zhang