Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 4 / 9E / b / iii

The upper-left block has characteristic and minimal polynomial $(x^2+1{)}^2$, while the lower-right block has characteristic and minimal polynomial $x^2+1$. Hence the corresponding module isIn the power bases from part (ii), an explicit normal form isthe direct sum of the companion matrices of $(x^2+1{)}^2$ and $x^2+1$.