The Hadamard Power of a matrix is the matrix consisting of all Hadamard products of subsets of its rows. We obtain several results concerning when a Hadamard Power has full column rank. This question in turn is central to the following problem: given a mixture of $k$ product distributions on a list of binary random variables $X_1,\ldots,X_n$, can the probability model be identified from the joint statistics of the $X_i$.

翻译：Hadamard 矩阵的力量是包含其行中子集的所有Hadamard产品的矩阵。 我们从Hadamard 力量何时拥有全列军衔获得若干结果。 这个问题反过来又对以下问题至关重要:鉴于二进制随机变量列表中的美元( X_ 1,\ldots, X_n$)的美元产品分配混合,能否从X_i美元联合统计中确定概率模型。