Converting immanants on singular symmetric matrices

M. A. Duffner, A. E. Guterman

Research output: Contribution to journalArticlepeer-review

Abstract

Let Σn(F) denote the space of all n×n symmetricmatrices over the complex field F, and χ be an irreducible character of Sn and dχ the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σn(F) → Σn(F) satisfying dχ(Φ(A) + αΦ(B)) = det(A + αB) for all singular matrices A, B ∈ Σn(F) and all scalars α ∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices.

Original languageEnglish
Pages (from-to)630-636
Number of pages7
JournalLobachevskii Journal of Mathematics
Volume38
Issue number4
DOIs
StatePublished - 1 Jul 2017
Externally publishedYes

Keywords

  • Determinant
  • converters
  • permanent
  • symmetric matrices

All Science Journal Classification (ASJC) codes

  • General Mathematics

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