題組內容

4. Let $T$ be the linear operator on $\mathsf{M}_{n \times n}(\mathbb{R})$ defined by $T(A) = A^t$.

(c) (8 pts) Find an ordered basis \( \beta \) for \( \mathsf{M}{n\times n}(\mathbb{R}) \) such that \( [T]{\beta} \) is a diagonal matrix.