Recent content by Muffins

Hahah, thanks Dick! I caught on a little late, but thanks a bunch for your reply!

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...