Consider two real nxn matrices A and B that are similar over C: That is, there is a
Chapter 7, Problem 43(choose chapter or problem)
Consider two real nxn matrices A and B that are similar over C: That is, there is a complex invertible nxn matrix S such that B = S~l AS. Show that A and B are in fact similar over R: That is, there is a real R such that B = R~lAR. (Hint: Write S = Sj + 1S2, where S\ and S2 are real. Consider the function / (z) = det(5j +z52), where z is a complex variable. Show that f(z) is a nonzero polynomial. Conclude that there is a real number* such that /(jc) ^ 0. Show that R = 5i +xS2 does the job.)
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer