Elementary bidiagonal factorizations
An elementary bidiagonal matrix is a square matrix such that every entry in the diagonal is \(1,\) exactly one entry either on the sub- or superdiagonal is nonzero, and all other entries are zero. The authors show that every \(n\times n\) matrix is a product of elementary bidiagonal matrices. For special cases, e.g., for \(2\times 2\) and \(3\times 3\) matrices they also determine the minimal number of factors needed in any elementary bidiagonal factorization.
scientific article; zbMATH DE number 1371374