Assume A is a 3x2 matrix with rank(A)=2. u1 and u2 are already left singular vectors... How would I go about proving that the cross-product of the two is also a left singular vector? Hints would be amazing, since I have no idea how to even approach the question. I'm assuming rank offers something significant to the question, but I don't see the correlation.
Thanks in advance!
There are 3 left singular vectors in $\mathbb{R}^3$, and they are all orthogonal to each other. You're given 2, so to find a 3rd vector which is orthogonal to both, you can use the cross product of the other two.