hi,everyone.I have a doubt.It regards the relations among real numbers ,vectors of R^n( n natural >1), matrices with real or complex inputs.i would like to know (even without proof) if :
a) taken a in R^n(n natual >0) , b in R^m(m natual >0) ,with n different from m,does it results a different from b ?
b) taken a in C^n(n natual >0) , b in R^(2*n) ,does it results a different from b ?
c)taken a in MR^(m,n)(m,n natua numbersl >0) , b in R^k(k natual >0) ,does it results a different from b ?
b)i know the proposition is true for n=1 because it results C=R^2 .For n >1 i only know there exists an oblivious bijection from C^n to R^(2*n),i.e. C^n and R^(2*n) have the same cardinality.
c) i paid attenction particulary on the case
c')m=n=1 , k=1
c'') n=1, k=m
Thanks to everyone could help me.Bye !