  We demonstrate a method for general linear optical networks that allows one
to factorize any SU($n$) matrix in terms of two SU($n-1)$ blocks coupled by an
SU(2) entangling beam splitter. The process can be recursively continued in an
efficient way, ending in a tidy arrangement of SU(2) transformations. The
method hinges only on a linear relationship between input and output states,
and can thus be applied to a variety of scenarios, such as microwaves,
acoustics, and quantum fields.
