Calculus Diagonalization

Question

Give an example of a 2×2 matrix with no real eigenvalues.

Answer 1

Let's the 2x2 matrix be (a b) the first raw and (c, d) the second raw. Write down the characteristic equation.

(a-λ)(d-λ)-bc=0.

From this equation you can find out how the coefficients a, b, c, d should be for the equation do not have real roots. That's it. you can write multiple examples of such matrices.