By the rules for transposing a matrix, the transpose of this
may be called the transpose of
the system . The transpose is obtained by interchanging
and in addition to transposing all matrices.
When there is only one input and output signal (the SISO case), is
a scalar, as is . In this case we have
That is, the transfer function of the transposed system is the
same as the untransposed system in the scalar case. It can be
shown that transposing the state-space representation is equivalent to
transposing the signal flow graph of the filter
. The equivalence of a flow graph to its transpose is
established by Mason's gain theorem [49,50].
See §9.1.3 for more on this topic.