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科学通报  2011 

矩阵的半张量积:一个便捷的新工具

DOI: 10.1360/972011-1262, PP. 2664-2674

Keywords: 半张量积,动态系统,布尔网络,李代数,生物系统,泛代数

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Abstract:

矩阵的半张量积是一种新的矩阵乘法.它将普通矩阵乘法推广到前阵列数与后阵行数不等的情况.推广后的乘法不仅保持了原矩阵乘法的主要性质,而且,具有伪交换性等比推广前更好的性质.因此,这是一个便捷而有力的新的数学工具.在简单介绍它的历史、定义和主要性质之后,本文对半张量积的本质及其优越性进行了分析,从而揭示它的合理性及有效性.接着,着重介绍它在若干领域的应用.包括(1)非线性(控制)系统的半张量积方法;(2)布尔网络的结构分析与控制;(3)半张量积在数学、物理中的其他应用.最后,本文对目前在研及可能突破的问题作了一个较详细的介绍,并对其潜在应用前景作了展望.

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