Consider the real linear map

Question

Question:

1. Fix α in H. Consider the real linear map

         M_α : H→H given by β→αβ

(a) With respect to the basis B = {1, i, j, k}, find the associated matrix for A_α for M_α .

(b) Find the associated matrix A (sub alpha bar) for M (sub alpha bar). Compare with (a).

(c) Compute det(A sub alpha) and det (A sub alpha bar). Interpret.