Question

give an example of a non-diagonalisable 4 x 4 matrix with eigenvalues -1,-1,1,1

Answer 1

Let Jordan canonical form is:

$$J = \left( \begin{array}{cccc} 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & 1 \\ 0 & 0 & 0 & -1 \end{array} \right).$$

It cannot de diagonalized.