矩陣半張量積與數(shù)學(xué)

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中圖分類(lèi)號(hào)：0151.21 文獻(xiàn)標(biāo)識(shí)碼：A

（中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院，北京100190）

Semi-tensor Product of Matrices and Mathematics

CHENG Daizhan (Academy of Mathematics and Systems Science,Chinese Academy of Sciences，Beijing lOol9o,China)

Abstract: After a brief review on the history of semi-tensor product (STP) of matrices，this survey paper introduces general definitions of STP and semi-tensor addition (STA），and the exploring researches on the mathematical essence of STP and STA，including three major branches: Modern Algebra，Geometry，and Analysis. The STP and STA，as cross-dimensional operators, enhance certain developments in classical mathematics，which is basically of fixed dimensions. As a survey paper, it mainly introduces fundamental concepts and basic results with few predictions. We hope to show such a fact that since the STP breaks the dimension barrier of matrix product, it will inevitably cause impact on the classical mathematics，which is of fixed dimensions.

Keywords: axiomatic semi-tensor product of matrices； super-group; universal manifold; superring；super-vector space; super-Lie group; super-Lie algebra

1 歷史的回顧

自從 2001年矩陣半張量積概念首次正式提出[1]，至今已歷 25年。（剩余29989字）