Define transformation T: R^3 -> R^3 by T(x)=Ax where A (3x3) matrix and has eigenvalues 5 and -2. Is A similar to a diagonal matrix? explain
If it has 2 eigenvalues then one of them has algebraic multiplicity equal 2. Let it be 5. Then if matrix of transformation has form 5 1 0 0 5 0 0 0 -2 then it is its Jordan form, and it cannot be diagonalized.