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, Representation
*This entry contributed by David Terr*

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## Cite this as:

Terr, David. "Faithful Representation." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/FaithfulRepresentation.html