标题： 使用流来阐明复数Hadamard矩阵空间的结构 显示英文标题

标题： Informing the structure of complex Hadamard matrix spaces using a flow

摘要： 复数Hadamard矩阵$H$的缺陷是来自$H$的连续Hadamard轨道维度的上界。 我们对缺陷提供了新的解释，即作为梯度流中心子空间的维度，并应用动力系统理论中的中心流形定理来研究复数Hadamard矩阵空间中的局部结构。 通过例子，我们提供了方法论的几个应用，包括Hadamard矩阵的仿射族的构造。 显示英文摘要

摘要： The defect of a complex Hadamard matrix $H$ is an upper bound for the dimension of a continuous Hadamard orbit stemming from $H$. We provide a new interpretation of the defect as the dimension of the center subspace of a gradient flow and apply the Center Manifold Theorem of dynamical systems theory to study local structure in spaces of complex Hadamard matrices. Through examples, we provide several applications of our methodology including the construction of affine families of Hadamard matrices.