 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-i/4/b/ii/solution

K = {A \in M_{n} (R) : A^{T} = - A} .

{E_{ij} - E_{ji} : 1 \leq i < j \leq n} .

Indeed, its diagonal entries vanish, and its entries below the diagonal are forced by those above it. Hence

dim K = (2 n)

. Part (a)(ii) proves that the only diagonalisable matrix in

K

0_{n}

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