/sci/ - Science & Math

>>15537435
Looks good to me.

>>15128487
>I'm not entirely sure of what I just wrote does it make any sense?
I'd say it's a very weird way to reason it out.
>And if it doesn't then why do non orthogonal eigenvectors imply a non orthogonally diagonalizable Matrix/endomorphism?
Because orthogonal diagonalizability implies the eigenvectors (of different eigenvalues) are orthogonal. You're looking at not B implies not A, but what you usually prove is A implies B (but apparently you haven't seen the result or forgot about it, hence the confusion).

If [math]A[/math] is symmetric, the vector [math]u[/math] has eigenvalue [math]\lambda_u[/math], [math]v[/math] has [math]\lambda_v[/math], then [math]\lambda_v u^T v = u^T A v = v^T A^T u = v^T A u = \lambda_u v^T u = \lambda_u u^T v[/math], hence either [math]u^T v = 0[/math] or [math]\lambda_u = \lambda_v[/math]