Shift again

1.

Shift the reduced matrix using the upper-left diagonal element.

2.

Perform QR iterations until an off-diagonal element gets below 10^-5.

3.

Extract the next eigenvalue, shift it back and confirm that it is one of the eigenvalues of A.

4.

Extract the $2 \times 2$ matrix in the upper left, and confirm that its eigenvalues are the remaining eigenvalues of A.