Show that the quadratic form 4x^2 + 2y^2 + 2z^2 − 2xy + 2yz − 2zx can be written as ~xT V ~x where ~x is a vector and where V is a symmetric matrix. Find the eigenvalues of V . Explain why, by rotating the

axes, the quadratic form may be reduced to the simple expression Ax'^2 + By'^2 + Cz'^2; what

are A, B, C?

I have done up to having found the eigenvalues, but am very confused about rotation matrices. Please help!