theorem ZM05Th59: :: ZMODUL07:21

for W, V being free finite-rank Z_Module
for A being Subset of V
for B being linearly-independent Subset of V
for T being linear-transformation of V,W
for l being Linear_Combination of B \ A st rank V = card B & A is Basis of (ker T) & A c= B holds
T . (Sum l) = Sum (T @* l)