A factorization of totally nonsingular matrices over a ring with identity
The authors call a rectangular matrix over a ring with identity totally nonsingular (TNS) if, for all \(k\), all its submatrices having either \(k\) consecutive rows and the first \(k\) columns, or \(k\) consecutive columns and the first \(k\) rows, are invertible. They prove that a matrix is TNS if and only if it admits a certain factorization with bidiagonal-type factors and certain invertible entries. This generalizes a recent result of the authors, namely the factorization of a square matrix over a ring with identity which satisfies the consecutive row and consecutive column properties.
scientific article; zbMATH DE number 1420038
scientific article