In this article we formulate an optimization problem of minimizing the distance from the uniform van der Waerden matrices to orthostochastic matrices of different orders. We find a lower bound for the number of stationary points of the minimization problem, which is connected to the number of possible partitions of a natural number. The existence of Hadamard matrices ensures the existence of global minimum orthostochastic matrices for such problems. The local minimum orthostochastic matrices have been obtained for all other orders except for 11 and 19. We explore the properties of Hadamard, conference and weighing matrices to obtain such minimizing orthostochastic matrices.

在本文中，我们提出了一个优化问题，以最小化统一范德华登矩阵与不同阶数的正交随机矩阵之间的距离。我们找到了最小化问题的固定点数量的下限，该下限与自然数的可能分区的数量有关。Hadamard矩阵的存在确保了此类问题的整体最小正随机矩阵的存在。除11和19外，所有其他阶次都获得了局部最小正则随机矩阵。我们探索Hadamard矩阵，会议矩阵和权重矩阵的属性，以获得此类最小化的正则随机矩阵。