Abstract
The authors [6] introduced the concept of a complete matrix of grade <TEX>$g$</TEX> > 3 to describe a structure theorem for complete intersections of grade <TEX>$g$</TEX> > 3. We show that a complete matrix can be used to construct the Eagon-Northcott complex [7]. Moreover, we prove that it is the minimal free resolution <TEX>$\mathbb{F}$</TEX> of a class of determinantal ideals of <TEX>$n{\times}(n+2)$</TEX> matrices <TEX>$X=(x_{ij})$</TEX> such that entries of each row of <TEX>$X=(x_{ij})$</TEX> form a regular sequence and the second differential map of <TEX>$\mathbb{F}$</TEX> is a matrix <TEX>$f$</TEX> defined by the complete matrices of grade <TEX>$n+2$</TEX>.
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