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 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 …

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 …

Can the determinant (assuming it's non-zero) be used to determine that the vectors given are linearly independent, span the subspace and are a basis of that subspace? (In other words assuming I hav...

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

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 …

Is there any difference between linear dependence, collinearity and coplanarity? Ask Question Asked 11 years, 10 months ago Modified 11 years, 10 months ago

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 …

Sep 10, 2023 · What is the integral closure of the integers in the real numbers? What is the integral closure of the ring $\mathbb {Z}$ inside the field $\mathbb {R}$ of real numbers and what are it's …

Sep 6, 2022 · More precisely, i cant understand what the next theorem stands for: Theorem 1.2 (on the continuous dependence of a solution on a parameter and on the initial flalues).