Let A be a matrix with real entries. Is it possible that Ran(A) = Null(At)? Does that change if it's a complex matrix?
Through browsing I've learned that the range of A should be orthogonal to the null space of A transposed, but I'm not sure how that exactly that is related to real vs. complex. We also haven't really gone over orthogonality in class (even though I am familiar to the concept), so theoretically this should be able to be solved without orthogonality.
I can see that a basis for the range of A relies on the pivot columns, and a basis for the null space of A transposed depends on the re-writing of the pivot rows of A transposed. I'm not sure how to proceed from here though. Thanks in advance!