an:06418269
Zbl 1320.15014
Ito, Hiroya; Noma, Atsushi; Ohno, Masahiro
Maximal minors of a matrix with linear form entries
EN
Linear Multilinear Algebra 63, No. 8, 1599-1606 (2015).
00342477
2015
j
15A54 15A15 13D02
maximal minors; polynomials; Eagon-Northcott complexes; Korn's inequality
Let \(P\) be a matrix whose entries are homogeneous polynomials in \(n\) variables of degree one over an algebraically closed field. The main theorem of this paper says that the maximal minors (say, \(m\)-minors) of \(P\) generate the linear space of homogeneous polynomials of degree \(m\) if \(P\) has the maximal rank \(m\) at every point of the affine \(n\)-space except for the origin. A counterexample shows that the result does not hold if the field is not algebraically closed.
Huajun Huang (Auburn)