Tangent cones to tensor train varieties (Q1638010)

The author presents a parametrization of the Bouligand tangent cone by showing that any vector in a given tangent cone can be written as an orthogonal sum of tensor train tensors. It is shown that the tangent cone of a tensor variety is the intersection of tangent cones of matrix varieties, and the set of defining equations of the tensor variety is the union of defining equations of matrix varieties of the appropriate matricizations.