1. The problem statement, all variables and given/known data If A is a rectangular n*m matrix (n>m) , and all the columns of A is orthonormal. I know that A'*A=I, where A' stands for its transpose. but A*A'<>I as I've learned from wiki. but is there an estimate for [tex]\|A \cdot A'\| [/tex]? 2. Relevant equations http://en.wikipedia.org/wiki/Orthogonal_matrix in the rectangular matrix section. 3. The attempt at a solution I have tried to write A in component form to find any hints. but i failed to solve the problem. but when i test A*A' , i always find that norm(A*A')=1, could you help me to explain it? Thank you in advance.