I want to decompose the following matrix using Cholesky. I know that $R=LL^T$ where L is the lower-triangular, but I do not know how to find the lower-triangular or if that formula suffices for this matrix
$$R = \begin{pmatrix} 1.0 & 0.6 & 0.4 & 0.2 \\ 0.6 & 1.0 &0.6 & 0.4 \\ 0.4 & 0.6 & 1.0 & 0.6 \\ 0.2 & 0.4 & 0.6 & 1.0 \end{pmatrix}$$
$R = $ $\begin{pmatrix} a_{11} & a_{21} & ... a_{n1} \\a_{21} & a_{22} & ... a_{n2} \\ a_{n1} & a_{n2} & ... a_{nn} \end{pmatrix}$
$L$ is the lower triangular matrix,
$\begin{pmatrix} \ell_{11} & 0 & ...0_n \\ \ell_{21} & \ell_{22} & ...0_n \\ \ell_{31} & \ell_{32} & ...\ell_{3n} \end{pmatrix}$
$L^T$ is the transpose of the above matrix.
$\ell_{ki} = \frac{\large a_{ki} - \displaystyle\sum_{j=1}^{i-1} \ell_{ij}*\ell_{kj}}{\huge\ell_{ii}}$
$\ell_{kk}= \sqrt{(a_{kk} - \displaystyle\sum_{j=1}^{k-1} (\ell_{kj})^2)} $