多维数阵的基阵和置换阵——处理复杂系统的新思维系列之二十一

Multilateral Matrix of Basic Matrix and Permutation Matrix——New Thinking of Dealing with Complex Systems Series Twenty-one

本系列论文基于《多边矩阵理论》,由东方整体性思维所启迪,试图提供并完善一套从整体到局部处理复杂系统多指标问题、非均匀性问题、非线性问题的强有力的数学工具,并对其进行严格的理论推导和证明。作为系列论文的第21篇,主要研究了多维数阵的基阵和置换阵。通过对基阵的定义和性质的研究,使多维数阵可以以基阵的形式表达并满足一些常见的运算。同时,通过基阵可以表达多维数阵的置换阵、指标置换多维数阵和换位置换多维数阵。

This series of articles, based on ＂Multilateral Matrix Theory＂ and inspired by the Eastern holistic thinking,are trying to provide and improve a set of powerful mathematical tools to handle multitarget local issues, non-uniformity problems and nonlinear problems of complex system ranging from the whole to the part with rigorous theoretical analysis and proof. As the twenty-first of the series, the mul- tilateral matrix of basic matrix and permutation matrix were studied. Through the research on the defi- nition and nature of basic matrix, the multilateral matrix can be conveyed in the form of basic matrix to meet some of the common operation, meanwhile, the multilateral permutation matrix, indicators permu- tation multilateral matrix and transposition permutation multilateral matrix can be implemented through the basic matrix.