An inverse matrix of an upper triangular matrix can be lower triangular
Copyright policy )An inverse matrix of an upper triangular matrix can be lower triangular
The definitions of two groups of matrices are discussed. One group consists of \(n\times n\) upper triangular matrices and is usually defined over a commutative ring. The second group is the full general linear group defined over any associative ring. Problems on a Dedekind finite ring and on the existence of a noncommutative ring \(R\) and two \(2\times 2\) matrices \(A\), \(B\) such that \(A\) is upper triangular, \(B\) lower triangular and \(AB=BA=1\) are treated.
- Polish Academy of Sciences Poland
- Silesian University of Technology Poland
- Institute of Mathematics Poland
commutative ring, Algebraic systems of matrices, invertible matrix, upper triangular matrices, Theory of matrix inversion and generalized inverses, group of matrices, Other matrix groups over rings, Dedekind finite ring
commutative ring, Algebraic systems of matrices, invertible matrix, upper triangular matrices, Theory of matrix inversion and generalized inverses, group of matrices, Other matrix groups over rings, Dedekind finite ring
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