• Corpus ID: 245385488

No short polynomials vanish on bounded rank matrices

  title={No short polynomials vanish on bounded rank matrices},
  author={Jan Draisma and Thomas Kahle and Finn Wiersig},
We show that the shortest nonzero polynomials vanishing on bounded-rank matrices and skew-symmetric matrices are the determinants and Pfaffians characterising the rank. Algebraically, this means that in the ideal generated by all t-minors or t-Pfaffians of a generic matrix or skew-symmetric matrix one cannot find any polynomial with fewer terms than those determinants or Pfaffians, respectively, and that those determinants and Pfaffians are essentially the only polynomials in the ideal with… 

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