A real binary tensor consists of 2^d real entries arranged into hypercube format 2^×d. For d = 2, a real binary tensor is a 2 × 2 matrix with two singular values. Their product is the determinant. We generalize this formula to d ≥ 2. Given a partition μ ⊢ d and a μ-symmetric real binary tensor t, we study the distance function from t to the variety X ^ℝ_μ of μ-symmetric real binary tensors of rank one. The study of the local minima of this function is related to the computation of the singular values of t. Denoting with the complexification of X ^ℝ_μ , the Euclidean Distance polynomial EDpoly \(_{X_\mu ^ \vee ,t}({\varepsilon ^2})\) of the dual variety of X_μ at t has among its roots the singular values of t. On one hand, the lowest coefficient of EDpoly \(_{X_\mu ^ \vee ,t}({\varepsilon ^2})\) is the square of the μ-discriminant of t times a product of sum of squares polynomials. On the other hand, we describe the variety of μ-symmetric binary tensors that do not admit the maximum number of singular values, counted with multiplicity. Finally, we compute symbolically all the coefficients of EDpoly \(_{X_\mu ^ \vee ,t}({\varepsilon ^2})\) for tensors of format 2 × 2 × 2.

一个实数二元张量由排列成超立方体格式 2 ^{× d}的 2 ^{d 个}实数项组成。对于d = 2，实二元张量是具有两个奇异值的 2 × 2 矩阵。他们的产品是决定因素。我们概括这个公式d ≥2.鉴于分区μ ⊢ d和μ -对称实际二进制张量吨，我们研究从距离函数吨到各种X ^ℝ _μ的μ秩一的-对称实际二进制张量。该函数局部极小值的研究与t奇异值的计算有关 . 用的复化表示X ^ℝ _μ，欧氏距离多项式EDpoly \（_ {X_ \亩^ \ V形，T}（{\ varepsilon ^ 2}）\）的双重各种X _μ在吨有它的根中t的奇异值。一方面，系数最低EDpoly的\（_ {X_ \亩^ \ V形，T}（{\ varepsilon ^ 2}）\）是的平方μ的-discriminant吨平方多项式的总和的时代的产物. 另一方面，我们描述了μ的多样性 - 对称二元张量，不允许最大数量的奇异值，用多重数计算。最后，我们符号化地计算格式为 2 × 2 × 2 的张量的EDpoly \(_{X_\mu ^ \vee ,t}({\varepsilon ^2})\) 的所有系数。