论文标题
固定多线性等级的张量的最小
Minimality of tensors of fixed multilinear rank
论文作者
论文摘要
我们发现了固定多线性（Tucker）等级的张量的几何特性。也就是说，固定多连线秩的实际张量形成了与Frobenius Inner产品的欧几里得空间的最小亚策略。我们还建立了仅限制在统计中的线性功能的线性功能的局部极值。
We discover a geometric property of the space of tensors of fixed multilinear (Tucker) rank. Namely, it is shown that real tensors of fixed multilinear rank form a minimal submanifold of the Euclidean space of tensors endowed with the Frobenius inner product. We also establish the absence of local extrema for linear functionals restricted to the submanifold of rank-one tensors, finding application in statistics.
