Drawing a parallel to linear Algebra.
Premise: The maximum of a determinate is when all the columns are orthogonal, given that the vectors are normalized.
Conclusion: The orthogonal trajectory should have a similar effect maximizing the wronskian. However, this does not seem to be true.
Given dy/dx = x
the orthogonal trajectory would seem to be -x
. However, this would show us that they are linearly dependent, and not maximized at all.
What is the definition of an "orthogonal function" as to orthogonal vectors? (functions whose tangent are orthogonal for every x
seemed like a reasonable definition ). Shouldn't such functions maximize the wronskian? How would one maximize the wronskian?