affine geometry - What does it mean to be affinely independent, and . . . 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 about linear (in)dependence: the points are linearly dependent iff there's not-all-zero coefficients $\alpha_i$ such that $\sum_i \alpha_i \mathbf p_i=0$ The points are linearly independent if this is not the case, that is
Exploring Sensitivity Dependence in Chaotic Systems 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 that can help us gain a deeper understanding of the nature of this system?
statistics - Why does one-hot encoding introduce linear dependence . . . With more than one categorical features, however, this changes quite a lot Already with a few one-hot encoded vectors you increase the probability to introduce linear dependence, with this probability becoming a certainty once the total columns in the design matrix exceed the number of samples
Weak vs Strong Dependency - Mathematics Stack Exchange 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 covariance each time, it should approach $0$
Does the solution depend on initial conditions? 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)