Editing Linear map (section)

===Monomorphism===
{{mvar|T}} is said to be ''[[injective]]'' or a ''[[monomorphism]]'' if any of the following equivalent conditions are true:
# {{mvar|T}} is [[injective|one-to-one]] as a map of [[set (mathematics)|sets]].
# {{math|1=ker ''T'' = {0<sub>''V''</sub>} }}
# {{math|1=dim(ker ''T'') = 0}}
# {{mvar|T}} is [[monic morphism|monic]] or left-cancellable, which is to say, for any vector space {{mvar|U}} and any pair of linear maps {{math|''R'': ''U'' → ''V''}} and {{math|''S'': ''U'' → ''V''}}, the equation {{math|1=''TR'' = ''TS''}} implies {{math|1=''R'' = ''S''}}.
# {{mvar|T}} is [[inverse (ring theory)|left-invertible]], which is to say there exists a linear map {{math|''S'': ''W'' → ''V''}} such that {{math|''ST''}} is the [[Identity function|identity map]] on {{mvar|V}}.