Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Decomposable Tensors as a Quadratic Variety

Robert Grone
Proceedings of the American Mathematical Society
Vol. 64, No. 2 (Jun., 1977), pp. 227-230
DOI: 10.2307/2041432
Stable URL: http://www.jstor.org/stable/2041432
Page Count: 4
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Decomposable Tensors as a Quadratic Variety
Preview not available

Abstract

Let $V_i$ be a finite dimensional vector space over a field $F$ for each $i = 1, 2, \ldots, m$, and let $z$ be a tensor in $V_1 \otimes \cdots \otimes V_m$. In this paper a set of homogeneous quadratic polynomials in the coordinates of $z$ is exhibited for which the associated variety is the set of decomposable tensors. In addition, a question concerning the maximal tensor rank in such a situation is answered, and an application to other symmetry classes of tensors is cited.

Page Thumbnails

  • Thumbnail: Page 
227
    227
  • Thumbnail: Page 
228
    228
  • Thumbnail: Page 
229
    229
  • Thumbnail: Page 
230
    230