Describe the Transpose of $A= \left[\matrix{0 & 0 & 1\\0 & 1 & 1\\ 1 &1 &1} \right]$

Question

$$A= \left[\matrix{0& 0& 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 1& 1& 1& 1\\ 0& 0& 0& 0& 0& 1& 1& 1& 1& 1\\ 0& 0& 0& 0& 1& 1& 1& 1& 1& 1\\ 0& 0& 0& 1& 1& 1& 1& 1& 1& 1\\ 0& 0& 1& 1& 1& 1& 1& 1& 1& 1\\ 0& 1& 1& 1& 1& 1& 1& 1& 1& 1\\ 1& 1& 1& 1& 1& 1& 1& 1& 1& 1\\ } \right]$$

Q: What does the spy(A') output look like? Describe?

I have been able to find A' (A Trnapose) in Matlab, and it looks identical to the original A matrix. However, I can't seem to figure out why I'm getting the original matrix back!

Answer 1

The transpose just takes each ith column of the original matrix and assigns it to the ith row of the transposed.

What does this do to your particular matrix?