Question

assume the matrix for a linear transfromation from V to W is known, also, the basis of W is known, can we find the corresponding basis in V. Does the procedure requiare the transformation be invertable?

Answer 1

so if we have {v1,v2,...,vn} as basis in V and we know some thransfomration maps them onto {w1,w2,..,wn). Do we need any other information or requairements besides the transformtaion matrix and the basis in W to calculate basis in V?