Stiefel-Whitney invariants for bilinear forms

Uriya A. First, Uzi Vishne

Research output: Contribution to journalArticlepeer-review

Abstract

We examine potential extensions of the Stiefel-Whitney invariants from quadratic forms to bilinear forms which are not necessarily symmetric. We show that as long as the symbolic nature of the invariants is maintained, some natural extensions carry only low dimensional information. In particular, the generic invariant on upper triangular matrices is equivalent to the dimension and determinant. Along the process, we show that every non-alternating matrix is congruent to an upper triangular matrix, and prove a version of Witt's Chain Lemma for upper-triangular bases. (The classical lemma holds for orthogonal bases.)

Original languageEnglish
Pages (from-to)1905-1917
Number of pages13
JournalLinear Algebra and Its Applications
Volume439
Issue number7
DOIs
StatePublished - 1 Oct 2013

Bibliographical note

Funding Information:
✩ This work was supported by the U.S.–Israel Binational Science Foundation (grant no. 2010/149).

Keywords

  • Bilinear form
  • Chain lemma
  • Milnor's K-ring
  • Quadratic form
  • Stiefel-Whitney invariant
  • Upper-triangular matrix

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