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 …

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...

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 linear (in)dependence As a brief …

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 …

Mar 22, 2017 · Finding Linear Dependence Relation Ask Question Asked 8 years, 9 months ago Modified 8 years, 9 months ago

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 …

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Jan 14, 2025 · I wrote a mildly lengthy explanation on this very recently regarding a similar problem. An easy way to see this is to consider one of the events in the intersections having probability $0$, then …