Question

If I have characteristics equation of a 4x4 matrix is \((x^2+1)^2\), what is the matrix? given that it has only 2 zeros entries on each row.
Please, help

Answer 1

@Freeboy15 @Kainui

Answer 2

The roots of the characteristic equation are the eigenvalues so your matrix has to be similar to the matrix with these eigenvalues on the diagonal. Specifically when I say similar I mean your matrix \(A\) is related to the diagonal matrix with eigenvalues on it \(D\) by:

\[A = P^{-1}DP\]

Your eigenvalues are i, i, -i, -i but I'm not sure if there's enough information given from the " given that it has only 2 zeros entries on each row." bit to figure it out or not. I'd probably try to pick a matrix P with variable entries or something to try to solve for it maybe? Not sure.