- #1
member 428835
Hi PF!
Given ##B u = \lambda A u## where ##A,B## are linear operators (matrices) and ##u## a function (vector) to be operated on with eigenvalue ##\lambda##, I read that the solution to this eigenvalue problem is equivalent to finding stationary values of ##(Bu,u)## subject to ##(Au,u)=1##, where ##(g,f) = \int fg##.
Can someone explain this to me, or point me in the right direction? I don't see how the two relate.
Given ##B u = \lambda A u## where ##A,B## are linear operators (matrices) and ##u## a function (vector) to be operated on with eigenvalue ##\lambda##, I read that the solution to this eigenvalue problem is equivalent to finding stationary values of ##(Bu,u)## subject to ##(Au,u)=1##, where ##(g,f) = \int fg##.
Can someone explain this to me, or point me in the right direction? I don't see how the two relate.