---- > [!definition] Definition. ([[linear isomorphism]]) > A **linear isomorphism** is a [[bijection|bijective]] [[linear map]]. > > Two [[vector space|vector spaces]] are [[isomorphism|isomorphic]] if there exists a [[linear isomorphism]] between them. ^definition > [!equivalence] > - [[the rank theorem for free modules|The dimension theorem]] and (as a special case with notably easier proof) [[the (finite) dimension theorem]]. ^equivalence ---- #### ---- #### 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 > ```