Thefollowingresultappliestolinearmapswithcontractingandexpandingbehaviour. Theorem:SupposethatAandBaretwonnmatrices,inducinginvertible hyperbolic linearmapsf(x)=Axandg(x)=BxonRn. Further,assume that1 (i) dimEu A=dimEu B, (ii) sgndet(A|Eu A )=sgndet(B|Eu B ) and (iii) sgndet(A|Es A )=sgndet(B|Es B ). 1A|Eu A denotesthematrixArestrictedtothe invariantsubspaceEu A. Condition(ii)saysthatf andg areeitherbothorientationpreservingor reversingwhenrestrictedtotheir respectiveunstablesubspaces. Condition(iii)hassimilarinterpretationforthestablesubspaces. Then: f and g are topologically conjugate