If then, for all we have:
But by hypothesis , so:
That is, .
I have this proof that I cannot figure out. If anyone could give me a little headstart that would be great. I am still struggling to fully grasp the concepts so maximum explanation is useful please.
Also I dont know how to make the perp symbol that looks like an upside down T so ill use an L instead.
W c V means W is a subspace of V
Suppose that A is a real symmetric n x n matrix. Show that if V is
a subspace of Rn and that A(V) c V, then A(V^L) c V^L.