Diagonalizing triangular matrices via orthogonal Pierce decompositions

• Author(s): Hartwig, Robert E. ; Patrício, Pedro ; Puystjens, Roland
• Date: 2005
• Persistent ID: http://hdl.handle.net/1822/1249
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Rings; Triangular matrices; Von Neumann regularity; Diagonalization
• Document Type: Article
• Language: English

Description

A class of sufficient conditions is given to ensure that the sum a+b in a ring R, is equivalent to a sum x + y, which is an orthogonal Pierce decomposition. This is then 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.