The matrix M has some interesting properties. It is used when simulating a portfolio of assets. The Cholesky decomposition separates a matrix E in two identical matrices M:
The matrix E is a matrix including the assets’ correlation.The matrix M is called Cholesky matrix. It is a lower triangular matrix. Multiplying the Cholesky matrix M with simulated random vectors will give linearly correlated random returns (see P.Wilmott, Derivatives , 1998, p.682).