A 2+2a = 0, which means that the eigenvalue of A satisfies λ 2+2λ = 0, so the eigenvalue is 0 and -2.

The eigenvalue of ka+e is kλ+ 1, namely 1 and 1-2k. Because the eigenvalues of positive definite matrices are all greater than 0, 1-2k >: 0 and k < 1/2.

So the value range of k is K.