theorem :: MATRLIN2:50

for K being Field
for V1, V2 being finite-dimensional VectSp of K
for b1 being OrdBasis of V1
for b2 being OrdBasis of V2
for f being linear-transformation of V1,V2 st dim V1 = dim V2 holds
( not ker f is trivial iff Det (AutEqMt (f,b1,b2)) = 0. K )