Singular value decomposition in Minkowski space (Q1911419)

Consider the real vector space \(\mathbb{R}^n\) endowed with a Minkowskian inner product. Let \(M\) be a real \(n\times n\) matrix. The author proves a criterion for the existence of a singular value decomposition of the form \(M= QDR\), where \(D\) is a diagonal matrix, while \(Q\) and \(R\) are orthogonal with respect to the given inner product. This result having been obtained, the existence of such a decomposition is discussed in case of timelike vector preserving matrices \(M\).