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On semi-tensor product of matrices and its applications. (English) Zbl 1059.15033
Similarly 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.

15A69 Multilinear algebra, tensor calculus
15A72 Vector and tensor algebra, theory of invariants
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
Full Text: DOI
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