In this work, we consider the p-almost Hadamard matrices and discuss about its connection with the orthogonal matrices corresponding to the finite projective planes, biplanes, triplanes, \(\lambda \)-planes, etc. Using multivariate analysis techniques, we obtain sufficient conditions for which such matrices are local optima to an optimization problem involving orthogonal matrix as constraints. Moreover, we establish sufficient conditions such that the quasi-orthogonal matrices like Mersenne matrices of level two are p-almost Hadamard matrices.

中文翻译：

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p-几乎Hadamard矩阵和$$ \ lambda $$λ-平面

在这项工作中，我们考虑了p-几乎Hadamard矩阵，并讨论了它与对应于有限投影平面，双平面，三平面，\（\ lambda \）平面等的正交矩阵的关系。对于这样的矩阵是以正交矩阵为约束的优化问题而言是局部最优的充分条件。此外，我们建立了充分的条件，以使准正交矩阵（如二级Mersenne矩阵）成为p-几乎Hadamard矩阵。