In $\mathbb{R}^2$, where $D = \{ [2, 1], [-2, 4] \}$ find the change of basis matrices from $D$ to $\mathcal{E}_2$ and from $\mathcal{E}_2$ to $D$.
I am having a hard time starting this problem because I do not know what $\mathcal{E}_2$ is. I am able to find information on changing from one basis to another where both are defined but not when using $\mathcal{E}_2$.
Can anybody point me in the right direction?
Edit: Based on the comments;
Does this mean the change of basis matrix for D to ε2 would be:
[2 -2]
[1 4]
And the change of basis matrix for ε2 to D would be:
[1 0]
[0 1]