Ok, I was reading the proof for Singular Value Decomposition in my Linear Algebra textbook, when the author made an assertion (without proof). Basically, he said that if A is an m x n matrix, then the nullspace of A is equal to the nullspace of transpose(A)*A. Now, it's obvious to me that any member of N(A) is in N(transpose(A)*A), since Ax=0 implies that transpose(A)*Ax=0. Nevertheless, I can't prove the converse of this statement to myself. Any tips?