Section 4.4

For equation (4.12), I assumed that s is a scalar number but if we are shifting the matrix why would a scalar number * an identity matrix be considered shifting a matrix since it would only change the entries along the diagonal. When you say that the Wilkinson shift has the additional benefit of naturally introducing complex numbers for initially real matrices does that mean that you are introducing a shift which is complex? The most difficult part was understanding the Function 4.1 (QR iteration with Wilkinson shift) completely. I understood quadratic convergencea little better.