In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃə.ˈlɛs.ki/) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.

#### Matlab Code

I’ve written this algorithm as matlab function which accepts one parameter as Matrix for Cholesky decomposition.

``````%Cholesky matrix decompression
function [retval] = Cholesky (A)
n = length( A );
L = zeros( n, n );
for i=1:n
L(i, i) = sqrt(A(i, i) - L(i, :)*L(i, :)');
for j=(i + 1):n
L(j, i) = (A(j, i) - L(i,:)*L(j ,:)')/L(i, i);
end
end
retval = L;
endfunction``````

#### Usage example

after creating Cholesky.m file, inside command window, call the function as below

``````A=[4 5 9;-2 6 0;1/2 6 10];
L=Cholesky(A)``````