论文标题
对角可高度形式和对称张量
Diagonalizable Higher Degree Forms and Symmetric Tensors
论文作者
论文摘要
我们提供了简单的标准和算法来表达同质多项式作为独立线性形式的幂之和，或等效地将对称张量分解为线性独立矢量的等级-1对称张量的总和。该标准依赖于两个高度形式的方面，即哈里森的代数理论和一些代数几何特性。所提出的算法是基本的，纯粹基于求解线性和二次方程。此外，作为我们标准和算法的副产品，人们可以轻松地决定均匀的多项式或对称张量是正交或单位分解的。
We provide simple criteria and algorithms for expressing homogeneous polynomials as sums of powers of independent linear forms, or equivalently, for decomposing symmetric tensors into sums of rank-1 symmetric tensors of linearly independent vectors. The criteria rely on two facets of higher degree forms, namely Harrison's algebraic theory and some algebro-geometric properties. The proposed algorithms are elementary and based purely on solving linear and quadratic equations. Moreover, as a byproduct of our criteria and algorithms one can easily decide whether or not a homogeneous polynomial or symmetric tensor is orthogonally or unitarily decomposable.
