×

zbMATH — the first resource for mathematics

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.

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)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abraham, R.A., Marsden, J.E. Foundations of Mechanics, 2nd ed. Benjamin/Cummings Pub. Com. Inc., 1978 · Zbl 0393.70001
[2] Cheng, D. Semi-tensor product of matrices and its application to Morgen’s problem. Science in China (Series F), 44(3):195–212 (2001) · Zbl 1125.15311
[3] Chern, S.S., Chen, W.H. Lecture notes on differential geometry. Beijing University Press, 1983 (in Chinese)
[4] Horn, R. Johnson, C. Topics in matrix analysis. Cambridge University Press, Cambridge, 1991 · Zbl 0729.15001
[5] Humphreys, J.E. Introduction to Lie algebras and representation theory. Springer-Verlag, New York, 1972 · Zbl 0254.17004
[6] Magnus, J.R., Neudecker, H. Matrix differential calculus with applications in statistics and econometrics. Revised Ed., John Wiley & Sons, Chichester, 1999 · Zbl 0912.15003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.