Ito, Hiroya; Noma, Atsushi; Ohno, Masahiro Maximal minors of a matrix with linear form entries. (English) Zbl 1320.15014 Linear Multilinear Algebra 63, No. 8, 1599-1606 (2015). 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. Reviewer: Huajun Huang (Auburn) MSC: 15A54 Matrices over function rings in one or more variables 15A15 Determinants, permanents, traces, other special matrix functions 13D02 Syzygies, resolutions, complexes and commutative rings Keywords:maximal minors; polynomials; Eagon-Northcott complexes; Korn’s inequality PDF BibTeX XML Cite \textit{H. Ito} et al., Linear Multilinear Algebra 63, No. 8, 1599--1606 (2015; Zbl 1320.15014) Full Text: DOI References: [1] DOI: 10.1007/978-3-642-10455-8 · Zbl 1246.35005 · doi:10.1007/978-3-642-10455-8 [2] Hartshorne R, Vol. 52 of graduate texts in mathematics (1977) [3] Atiyah MF, Introduction to commutative algebra (1969) [4] DOI: 10.1007/978-3-642-18808-4 · doi:10.1007/978-3-642-18808-4 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.