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Bookmark or Share- 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 linear (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 $\sum_i \alpha_i \mathbf p_i=0$.
- matrices - How to determine whether there is a linear dependence ...If there are more rows than columns, it is less straightforward to detect a dependence between the columns. You can take the square matrix comprised of the first rows and all the columns, and if the determinant is zero, there may be a dependence (the dependence in the square matrix has to extend consistently - but the dependence in the top ...
- Connection between linear independence, non-/trivial and x solutions ...a31x1 + a32x2 + a33x3 = 0; The homogeneous linear system has the two kinds of solutions. 1). zero solution. The sufficient and necessary condition of the zero solution for is listed as follows: det(A) ≠ 0; 2). Non-zero solution: The sufficient and necessary condition of the zero solution is listed as follow: det(A) = 0;
- What exactly does linear dependence and linear independence imply ...A broader perspective on linear dependence is the theory of relations in group theory. Roughly speaking, a relation is some equation satisfied by the elements of a group, e.g. $(ab)^{-1}=b^{-1}a^{-1}$; relations basically amount to declaring how group elements depend on each other.
- Finding Linear Dependence Relation - Mathematics Stack Exchange1. (I don't have enough reputation to post a comment, so posting it as here) one way to find the dependency is track your row reduction steps. For example if these are the steps that reduced the matrix. R1 = R2 - R1 , R3 = R3 - R1, R3 = R3 + 2R2. Now R3 = R3 + 2R2 replace R3 and R2 from first two steps.
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