6.2 LU factorization

Let

$A_{n\times n}$ - fully occupied matrix, rowise stored,
$L$ - lower triangular matrix with normalization $\ell_{i,i}=1$, column-wise stored,
$U$ - upper triangular matrix, rowise stored,

and $\sum\limits_{j=1}^n \ell_{i,j} \cdot u_{j,k} = a_{i,k}$ is hold.