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 …

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 …

May 2, 2017 · Affine (in)dependence We say that a set of points {pi}m i=1 {p i} i = 1 m is linearly dependent if its linear span is generated by a strict subset of the points. Equivalently, if its linear span …

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 …

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

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

Here are two possibilities. One is geometric. If the columns of a square matrix are linearly dependent, the image of the unit cube under the transformation has measure zero, so $\det (A) = 0$. Here is …

Feb 3, 2023 · We know that the solution to the wave equation in the domain of dependence is solely determined by the initial values. Now, if the boundary is outside the domain of dependence the …

Jul 16, 2017 · Independent is the lack of any dependence. So if there is even the tiniest dependence (between only a subset of the vectors), the whole set of vectors is dependent. Your proposed …

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