On semi-tensor product of matrices and its applications.

*(English)*Zbl 1059.15033Similarly to the left semi-tensor product the authors introduce the right semi-tensor product. Certain properties are presented. The major differences between the left and the right semi-tensor products are discussed. Then two new applications are investigated. The first one is its application to the connection. The evaluation of a connection is expressed by a matrix multiplication. The Christoffel symbols are arranged as a matrix. Its conversion under a coordinate transformation is presented by matrix products. Some of its applications are also revealed there. Then the authors consider its applications to finite-dimensional Lie algebras. Certain properties of the algebra are described by matrix forms.

Reviewer: Yueh-er Kuo (Knoxville)

##### MSC:

15A69 | Multilinear algebra, tensor calculus |

15A72 | Vector and tensor algebra, theory of invariants |

17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |

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\textit{D. Cheng} and \textit{L. Zhang}, Acta Math. Appl. Sin., Engl. Ser. 19, No. 2, 219--228 (2003; Zbl 1059.15033)

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##### References:

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