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Abstract: On the set of mappings of the given set, we define the product of mappings.If A is associative algebra, then we consider the set of matrices, whoseelements are linear mappings of algebra A. In algebra of matrices of linearmappings we define the operation of product. The operation is based on theproduct of mappings.If the matrix a of linear mappings has an inverse matrix, then thequasideterminant of the matrix a and the inverse matrix are matrices of linearmappings. In the paper, I consider conditions when a matrix of linear mappingshas inverse matrix, as well methods of solving a system of linear equations inan associative algebra.



Author: Aleks Kleyn

Source: https://arxiv.org/







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