# Linear Flows ```toc ``` $f[h] = \beta+ \Omega h$ - the determinant of the jacobian is the determinant of $\Omega$ - One way to make a linear flow that is general, efficient to invert, and for which the Jacobian can be computed efficiently is to parameterize it directly in terms of the LU decomposition - $\Omega= PL(U + D)$ - where P is a predetermined permutation matrix, L is a lower triangular matrix, U is an upper triangular matrix with zeros on the diagonal, and D is a diagonal matrix that supplies those missing diagonal elements