Abstract
Abstract The determinantal variety Σ p q {\Sigma_{pq}} is defined to be the set of all p × q {p\times q} real matrices with p ≥ q {p\geq q} whose ranks are strictly smaller than q. It is proved that Σ p q {\Sigma_{pq}} is a minimal cone in ℝ p q {\mathbb{R}^{pq}} and all its strata are regular minimal submanifolds.
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