Transposing a Matrix

What is the problem

Given a Matrix

$$A=\left[\begin{array}{cccc}\uparrow & \uparrow & & \uparrow \\ {\vec{a}}_0& {\vec{a}}_1& ⋮& {\vec{a}}_n\\ \downarrow & \downarrow & & \downarrow \end{array}\right]$$

(by convention, $A$ is always a columns matrix)
Find its transposed rows matrix.

Strategy

Starting from the farthest/rightmost vector:

1. Rotate it anti-clockwise $\circlearrowleft$
   
   (Do the same for the next vector, and then the one after it (moving to the left), but raise each one a bit after rotation)
2. (…)
   
3. (${\vec{a}}_1$)
   
4. (${\vec{a}}_0$)
   
5. Finally, Squish them all into a row vector.
   

Connections