Mastering Python for Finance - Second Edition

The Cholesky decomposition

The Cholesky decomposition is another way of solving systems of linear equations. It can be significantly faster and uses a lot less memory than the LU decomposition, by exploiting the property of symmetric matrices. However, the matrix being decomposed must be Hermitian (or real-valued symmetric and thus square) and positive definite. This means that the A matrix is decomposed as A=LL^T, where L is a lower triangular matrix with real and positive numbers on the diagonals, and L^T is the conjugate transpose of L.

Let's consider another example of a system of linear equations where the A matrix is both Hermitian and positive definite. Again, the equation is in the form of Ax=B, where A and B take the following values: ...