Every unit matrix is a LULU
This paper is devoted to prove that every unit matrix \(A\) (i.e. every matrix with determinant one) has a factorization of the form \(A=L_0 U_0 L_1 U_1\), where the four matrices are triangular with ones on their diagonal (\(L_i\) are lower triangular, and \(U_i\) are upper triangular). The paper should be read in connection to \textit{T. Toffoli}'s paper [ibid. 259, 31-38 (1997; Zbl 0893.15004)] where a related result, motivated with examples from computer graphics, is stated. In the paper under review, the author proves the existence of a factorization as a product of four triangular matrices for every unit matrix (not almost every). In addition, it should be mentioned that the problem of finding an efficient method to construct the factorization (``a minimal adjustment'' in the author's words) remains open.
scientific article; zbMATH DE number 1076376