Diagonalizing triangular matrices via orthogonal Pierce decompositions
Sufficient conditions are derived under which the sum \(m\) = \(a\) + \(b\) in a ring \(R\), with \(a\) regular, is equivalent to a sum \(n\) = \(e\)\(n\)\(f\) + (1 - \(e\))\(n\) (1 - \(f\)), which admits an orthogonal Pierce decomposition, for suitable idempotents \(e\) and \(f\). These results are used to show that a lower triangular matrix, with \(a\) regular diagonal, is equivalent to its diagonal iff the matrix admits a lower triangular von Neumann inverse.
scientific article; zbMATH DE number 2173159