Never mind! I found the actual theorem on the web, and I think this is pretty much what I was looking for anyway
Consider the polynomial
f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real)
where all a*x are real. The equation f(x) = 0 is thus
a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+...
Homework Statement
Suppose that f(x) is a polynomial of degree n with real coefficients; that is,
f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real)
Suppose that c ∈ C(complex) is a root of f(x). Prove that c conjugate is also a root of f(x)
Homework Equations...
So something like this?
We want to show that w is a linear combination of (Sv1, Sv2, ... ,Svg)
which says we have
c1*S*v1 + c2*S*v2 + ... + cg*S*vg = w
we can pull out the S...
S(c1v1 + c2v2 + ... + cgvg) = w
S^-1(S(c1v1 + c2v2 + ... + cgvg) = S^-1*w
(c1v1 + c2v2 + ... + cgvg)...
Homework Statement
Suppose A and B are similar matrices, and that (mu) is an eigenvalue of A. We know that (mu) is also an eigenvalue of B, with the same algebraic multiplicity(proved in class) Suppose that g is the geometric multiplicity of (mu), as an eigenvalue of B. Show that (mu) has...