---- > [!definition] Definition. ([[faithful group representation]]) > A [[group representation]] is said to be **faithful** if the corresponding [[group action]] is [[faithful group action|faithful]] — i.e., the corresponding [[group homomorphism|homomorphism]] into $\text{GL}(V)$ [[homomorphism induced by group action|is an]] [[injection]]. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```