/sci/ - Science & Math

>>11996989
The usual. Got some stuff to solve. The kind of stuff which you can't go and just mechanically solve yourself, it actually requires some form or another of human interaction.
Currently studying C++ programming.
How about you? Doing anything in particular?

>>11305741
I don't have a solution, but I do have some intermediary results.
[math]A( \phi + A \phi )= A \phi + AA \phi = \phi + A \phi[/math]
[math]A( \phi - A \phi )= A \phi - AA \phi = A \phi - \phi [/math]
This lets us give any [math]\phi [/math] as a sum of two eigenvectors of [math]A[/math], specifically [math]\frac{ \phi + A \phi}{2} + \frac{\phi - A \phi}{2}[/math].
There are some conditions on eingenvectors which essentially implies that [math]A[/math] and [math]B[/math] just swap around eigenvectors.
Specifically, assuming [math]A \phi = \phi [/math] (which is, by the way, one of the only two possible cases for eigenvalues), then we have [math]0= (AB + BA) \phi = AB \phi + B \phi [/math]. Then,
[eqn] AB \phi = -B \phi[/eqn]
Setting [math]\psi = B \phi[/math], we reach
[eqn] A \psi = - \psi [/math].
>book recs
My bad, don't have anything in particular.

Official notation ranking:
Newton multivarible>Euler>Lagrange single variable>Newton single variable>Leibniz>Lagrange multivariable.