Recent content by Fringhe

Ok for the first question, two lts B and C are equivalent iff there exist lts E and F such that B = E^-1 C F Now let E = P and let F=Q, we have B= P^-1 C Q or PB = CQ so this means that the lts P and Q must be invertible?

Homework Statement 1) two linear transformations B and C are equivalent iff there exist invertible linear transformations P and Q such that PB=CQ 2) if A and B are equivalent then so are A' and B' in dual space 3) Do there exist linear transformations A and B such that A and B are equivalent...

Homework Statement How could I prove that the subset of a finite dimensional space is also finite dimensional? Homework Equations N/A The Attempt at a Solution I think it's more intuitive in the sense that since the vector space is finite dimensional the subset is forcibly finite...

Ok, so let x=(\xi1,\xi2,\xi3) (where \xi1=\xi2) and let y be the functional such that y = \xi1+\xi2+0*\xi3 So for xi (i from 0 to n) y(xi) would equal 0.

Homework Statement Define a non-zero linear functional y on C^2 such that if x1=(1,1,1) and x2=(1,1,-1), then [x1,y]=[x2,y]=0. Homework Equations N/A The Attempt at a Solution Le X = {x1,x2,...,xn} be a basis in C3 whose first m elements are in M (and form a basis in M). Let X' be...