# Finding a matrix to represent a 2x2 transpose mapping

1. Oct 27, 2015

### PsychonautQQ

1. The problem statement, all variables and given/known data
Let L be a mapping such that L(A) = A^t, the transpose mapping. Find a matrix representing L with respect to the standard basis [1,1,1,1]

2. Relevant equations

3. The attempt at a solution
So should I end up getting a 4x4 matrix here? I got 1,0,0,0 for the first column, 0,0,1,0 for the second column, 0,1,0,0 for the third column and 0,0,0,1 for the fourth column. is this correct?

2. Oct 27, 2015

### Staff: Mentor

How is [1, 1, 1, 1] a basis?
I think you mean {<1, 0, 0, 0>, <0, 1, 0, 0>, <0, 0, 1, 0>, <0, 0, 0, 1>}.
This works, if it's legitimate to work with vectors in $\mathbb{R}^4$ instead of 2 x 2 matrices. Of course $\mathbb{M}_{2 x 2}$ is isomorphic to $\mathbb{R}^4$. Based on what I think the problem statement is supposed to mean, your solution looks fine.