Question

problem 6

15 UTU ..). We recall that if T whose (ij)th component oponent is ; Tija). The tained by interchanging Consider the proof of THCTUM ises 6-8 deal with k xk complex matrices T = (Tu). We ter S = (S. :) are k x k matrices, TS is the matrix whose lii (T) and S = (Sij) are and ifs Eck Ta is the vector whose ith component is adioint of the matrix T is the matrix Tº obtained by rows and columns and taking complex conjugates, that is, (7), 6. Show that (Ta, b) = (a, T*b) for all a, beck. the "product" defined by (a, b)t = (Ta, b) satisfies properties (3.3) and (3.4). 9. Show that if I = TG.).

Answer 1

T= (11) - 268 To, b) = compleu matuix. Ta= {Tijaj 8 tj aj). bi - a. CTibi) a, b , concle Tt is the adjoint of the matura Hencen (Ta, 6) = a, Ttb) tabt C