I have a very hard time remembering which is which between linear independence and linear dependence... that is, if I am asked to specify whether a set of vectors are linearly dependent or …

Nov 9, 2024 · Strictly speaking, it's an affine linear dependence since the sum of the one-hot features is the constant feature $\mathbf {1} = [1\,1\,1\,\cdots\,1]^\top$. This means that if you know all but one …

Oct 8, 2023 · My question is, are there any other methods or techniques to investigate the sensitivity dependence of orbits for this map in more detail? Are there additional metrics or mathematical tools …

Functional dependence means left-total and single-valued relation. Differential structure is not part of the definition.

Dec 27, 2025 · I have written tons of answers about the notation behind partial detivatives and the Euler-Lagrange equations. But what is your question here? They seem too spread out among a wall of …

May 2, 2017 · Here's the main ideas relating linear and affine (in)dependence: Let $\mathbf p_i\in\mathbb {R}^d$ be points in a real space. Reminder of (in)dependence As a brief reminder …

Dec 16, 2024 · For the purposes of differential geometry I would like to fully process the basics of ODEs, namely the existence/uniqueness theorem (EUT) and continuous/smooth dependence on initial …

Nov 2, 2021 · How can I see the connection between the continuity of that flow and this continuous dependence on the initial conditions? This is what puzzles me because they should define the same …

Jun 9, 2019 · Weak dependence primarily appears as a technical condition in various probabilistic limit theorems. -Wikipedia So basically if we keep testing the variables over and over again and compute …

Apr 11, 2018 · I am fairly new to stochastic calculus and trying to get to grips with the concept and in particular how the notation is representing the time dependence. I summarise my understanding to …