Question

How to find similar matrix to under real field repeating eigenvalue not diagonalisable

Answer 1

The geometric multiplicity of an eigenvalue (that is, the number of independent eigenvectors corresponding to that eigenvalue), is the dimension of the null space of the matrix minus the identity matrix times that eigenvalue (that is, you take the matrix and subtract the eigenvalue from each main diagonal entry). The dimension of the null space of a n×n matrix is n minus the rank of the matrix. So if n=2, then to have a geometric multiplicity of 2, you have to have the rank be zero. But a rank zero matrix is simply he zero matrix. So once you subtract 2 from the main diagonal and see that you don't get the zero matrix, you know that there's only one linearly independent eigenvector for that eigenvalue.

Answer 2

Hey

I love you. I love you.