  Time-Delay Interferometry (TDI) is the data processing technique that cancels
the large laser phase fluctuations affecting the one-way Doppler measurements
made by unequal-arm space-based gravitational wave interferometers. By taking
finite linear combinations of properly time-shifted Doppler measurements, laser
phase fluctuations are removed at any time t and gravitational wave signals can
be studied at a requisite level of sensitivity. In the past, other approaches
to this problem have been proposed. Recently, matrix based approaches have been
put forward; two such approaches are by Vallisneri et al. and Tinto, Dhurandhar
and Joshi. In this paper we establish a close relationship between these
approaches. In fact we show that the matrices involved in defining the
operators in the two approaches exhibit an isomorphism and therefore in both
approaches one is dealing with matrix representations of the time-delay
operators.
