Recent content by steinmasta

Homework Statement Suppose A is a real symmetric 3 × 3 matrix such that • trace(A) = 0 • R(LA) = span {(1, 1, 1) and (1, 0, -1)} (sorry for formatting issues - these are both column vectors) where La is the left multiplication transformation • A * (1, 1, 1) = (2, 1, 0) again, these...

Regarding 1, I have tried to show that UT is self-adjoint with respect to the inner product <x,y>' = <T(x),y> but I've had trouble unwinding definitions. Regarding 2a, I tried to show that if U commutes with T, then U commutes with T*. This corollary to the spectral theorem is useful: If F...

I have two questions: 1. Let V be a finite dimensional inner product space. Show that if U: V--->V is self-adjoint and T: V---->V is positive definite, then UT and TU are diagonalizable operators with only real eigenvalues. 2. Suppose T and U are normal operators on a finite dimensional...