MATLAB Language Matrix decompositions Cholesky decomposition


The Cholesky decomposition is a method to decompose an hermitean, positiv definite matrix into an upper triangular matrix and its transpose. It can be used to solve linear equations systems and and is around twice as fast as LU-decomposition.

A = [4 12 -16
    12 37 -43
    -16 -43 98];
R = chol(A);

This returns the upper triangular matrix. The lower one is obtained by transposition.

L = R';

We finally can check whether the decomposition was correct.

b = (A == L*R);