The result of an operation on a function is another function, therefore we can naturally apply an operator on another operator. In other words, if
,
are two operators, then we can define
as
, provided that
makes sense mathematically. This is called the composition of the operators
and
. Because in the discrete case the composition of operators is in fact the multiplication
of the two matrices
,
the operator composition is usually referred to as operator product and denoted by
is used. The composition of operators can be naturally extended to any finite product
. The product of up to 3 operators is implemented in [sec:chain]chain.c.