How do I go about diagonalizing such a matrix.
For example let $D$ be the quaternion algebra over $\mathbb{Q}$ with $i^2 = -1, j^2 = -11$ and take the matrix:
$A = \begin{pmatrix} 11 & -j-3k \\ j+3k & 11 \end{pmatrix}$.
How do I find $P\in$ $GL_2(D)$ such that $\bar{P}^T A P$ is diagonal? Does the non-commutativity create problems with the usual construction?