So, I have this question that I'm having a lot of trouble understanding.
Let $f:\mathbb{R}^4\rightarrow\mathbb{R}^4$ be a linear map defined by $f(e_i)=ie_i$ for $1\leq i\leq 4$ where $(e_1 \ldots,e_4)=I_4$ and let $$ H=\begin{pmatrix}1 & 1 & 1 & 1 \cr 1 & -1 & 1 & -1 \cr 1 & 1 & -1 & -1 \cr 1 & -1 & -1 & 1 \cr\end{pmatrix}.$$ Find the matrix of $f$ under the basis $H$ of $\mathbb{R}^4$.