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 …

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 …

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 …

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

Is there any difference between linear dependence, collinearity and coplanarity? Ask Question Asked 11 years, 11 months ago Modified 11 years, 11 months ago

Aug 14, 2019 · If there is a constant linear dependence between the functions, it also occurs between their derivatives and between their second derivatives. So assume a constant linear dependence, …

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 …