TY - JOUR
T1 - On maximum, typical and generic ranks
AU - Blekherman, Grigoriy
AU - Teitler, Zach
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2015/12/3
Y1 - 2015/12/3
N2 - We show that for several notions of rank including tensor rank, Waring rank, and generalized rank with respect to a projective variety, the maximum value of rank is at most twice the generic rank. We show that over the real numbers, the maximum value of the real rank is at most twice the smallest typical rank, which is equal to the (complex) generic rank.
AB - We show that for several notions of rank including tensor rank, Waring rank, and generalized rank with respect to a projective variety, the maximum value of rank is at most twice the generic rank. We show that over the real numbers, the maximum value of the real rank is at most twice the smallest typical rank, which is equal to the (complex) generic rank.
KW - 14N15
KW - 15A21
KW - 15A69
UR - http://www.scopus.com/inward/record.url?scp=84937526056&partnerID=8YFLogxK
U2 - 10.1007/s00208-014-1150-3
DO - 10.1007/s00208-014-1150-3
M3 - Article
AN - SCOPUS:84937526056
SN - 0025-5831
VL - 362
SP - 1021
EP - 1031
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3-4
ER -