Two homework questions (they are due in four days, dang) that's bugging me :
1. Let F be a commuting family of diagonalizable normal operators on a finite dimensional inner product space V and A0, the self-adjoint algebra generated by F. Let A be the self-adjoint algebra generated by F and the identity operator I. Show that there is at most one root T of A such that r(T) = 0 for all T in A0. (From Hoffman and Kunze, if that help). I tried the normal operator and spectral theory, but I'm a little rusty on my linear algrabra so...
2. By considering the work done to alter adiabatically the length "l" of a plane pendulum, prove by elementary means the adiabatic invariance of "J" for the plane pendulum in the limit of vanishing amplitude. (Goldstein, if that help). Off course I can do it with a PDE, but with elementary means, I have no clue.
Two homework questions (they are due in four days, dang) that's bugging me :
1. Let F be a commuting family of diagonalizable normal operators on a finite dimensional inner product space V and A0, the self-adjoint algebra generated by F. Let A be the self-adjoint algebra generated by F and the identity operator I. Show that there is at most one root T of A such that r(T) = 0 for all T in A0. (From Hoffman and Kunze, if that help). I tried the normal operator and spectral theory, but I'm a little rusty on my linear algrabra so...
2. By considering the work done to alter adiabatically the length "l" of a plane pendulum, prove by elementary means the adiabatic invariance of "J" for the plane pendulum in the limit of vanishing amplitude. (Goldstein, if that help). Off course I can do it with a PDE, but with elementary means, I have no clue.
Your name is Markus
Forget about my questions you're just too dumb
Dude, study social sciences, free yourself from this crap.
Two homework questions (they are due in four days, dang) that's bugging me :
1. Let F be a commuting family of diagonalizable normal operators on a finite dimensional inner product space V and A0, the self-adjoint algebra generated by F. Let A be the self-adjoint algebra generated by F and the identity operator I. Show that there is at most one root T of A such that r(T) = 0 for all T in A0. (From Hoffman and Kunze, if that help). I tried the normal operator and spectral theory, but I'm a little rusty on my linear algrabra so...
2. By considering the work done to alter adiabatically the length "l" of a plane pendulum, prove by elementary means the adiabatic invariance of "J" for the plane pendulum in the limit of vanishing amplitude. (Goldstein, if that help). Off course I can do it with a PDE, but with elementary means, I have no clue.
Grim and brutal in bathroom. Taken with shitty cellphone camera.