Matrix factorisations such as the \(L\,R\) decomposition, \(A = P\, L\,R\) , the \(Q\,R\) decomposition, \(A = Q\, R\) , the diagonalisation \(A= B \, D \, B^{-1}\) are advantageous in various applications in engineering mathematics. In this chapter, we discuss further factorisations, namely the Schur decomposition and the singular value decomposition of a matrix A. These decompositions find applications in numerical mathematics, but also in signal and image processing. Both methods build on well-known concepts and therefore also repeat many concepts developed in earlier chapters on linear algebra. We formulate these factorisations in a recipe-like manner, drawing on earlier recipes.