A representation 
of a group 
is faithful if it is one-to-one,
i.e., if 
implies 
for 
.
Equivalently, 
is faithful if 
implies 
,
where 
is the dimension of 
, 
is the 
identity matrix,
and 
is the identity element of 
.
Faithful Representation
See also
Faithful, RepresentationThis entry contributed by David Terr
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Terr, David. "Faithful Representation." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FaithfulRepresentation.html