i am a newbie to linear algebra
My question is
Let T of dimension mxn, be a linear map from A -> B. if n<m and rank of T is n, which basically means all of the vector space A is mapped,and null space is empty. Then why there is no inverse for T??
My understanding is that for A_inv to exist, all the vector space B should be one to one mapped back to A. This is not possible because vector space B is of high dimension(m) and thus have more elements than A, which is of low dimension(n).
Is this view right??
