I know that the three eigenvalues of the real third order matrix A
are -1
, 1
, 1
, and the eigenvector corresponding to eigenvalue -1
is $(0,1,1)^T$. I want to find a matrix A
that meets the requirements.
A = Array[x, {3, 3}];
FindInstance[(Eigenvalues[A] == {-1, 1,
1}) && (A.{{0, 1, 1}}\[Transpose] == -1*{{0, 1, 1}}\[Transpose]) , Flatten[A], Reals]
But the above code returns an empty set. What can I do to find some matrices that meet the constraints?