Question

Let A*=A. Show that all eigenvalues of A are real.

Please be NEAT and show all work, and please explain what you're doing because I am trying to understand this material. Thank you.

Answer 1

I Solution given Ax= A Then we all eigen value of show let it be for the x be To and Then have to schow are real eigen value eigen vector nx = dy Now - Axxix How from Inner produrd (X1AX) = (X, 1 x) = 6 xcxix) - 0 and CX AX E CAXX ) =cax,x) - Tlxix) (1) from equation and -) x(x,x) - I LXIX) = (x-7)(x,x)=0 = dat u. (x,x) to which se pocsible only & are real I all eigen value are له)