In this paper, some conditions for the nonsingularity and group inverses of linear combinations of generalized and hypergeneralized projectors are established. Moreover, some formulae for the inverses and group invers...In this paper, some conditions for the nonsingularity and group inverses of linear combinations of generalized and hypergeneralized projectors are established. Moreover, some formulae for the inverses and group inverses of them are derived. The work of this paper extends some previous results.展开更多
The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of hypermatrices.The product is first defined for three-dimensional hypermatrices with compatible orders an...The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of hypermatrices.The product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general cases.Three different types of hyperdeterminants are introduced and certain properties are revealed.The Lie groups and Lie algebras corresponding to the hypermatrix products are constructed.Finally,these results are applied to dynamical systems.展开更多
基金Supported by the National Natural Science Foundation of China(11271105)the Key Research Project of Educational Department of Hubei Province(D20122202)Youth Research Project of Educational Department of Hubei Province(B20122203)
文摘In this paper, some conditions for the nonsingularity and group inverses of linear combinations of generalized and hypergeneralized projectors are established. Moreover, some formulae for the inverses and group inverses of them are derived. The work of this paper extends some previous results.
基金supported partly by the National Natural Science Foundation of China under Grant Nos.62073315 and 62103305Shanghai Pujiang Program under Grant No.21PJ 1413100China Postdoctoral Science Foundation under Grant Nos.2021M703423 and 2022T150686。
文摘The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of hypermatrices.The product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general cases.Three different types of hyperdeterminants are introduced and certain properties are revealed.The Lie groups and Lie algebras corresponding to the hypermatrix products are constructed.Finally,these results are applied to dynamical systems.
