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Bookmark or Share- linear algebra - Determine if vectors are linearly independent ...Firstly, you are to arrange the vectors in a matrix form the reduce them to a row-reduced echelon form. (If the last row becomes all zeros then it is linearly dependent, but if the last row isn't all zeros then it is linearly independent).
- partial differential equations - Continuous dependence of the solution ...I am looking the following: What do we mean by the sentence "continuous dependence of the solution of the heat equation from the initial data, on the interval $[0,2\\pi]$ with Dirichlet boundary d...
- vectors - Is there any difference between linear dependence ...Given another vector which is in the span of these vectors, it is "coplanar" with them (in the same plane). So being coplanar does mean linear dependence (to the basis of a given plane). Colinear is the same idea but more general, the dependence doesn't have to be in a plane, it can be a hyperplane etc.
- 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.
- linear algebra - Intuition behind functional dependence - Mathematics ...Maybe you could make that an answer, as I have the impression, that you have a deeper understand of functional (in)dependence (and how it generalizes linear (in)dependence) and the answer already give does not yet cover all concerns. $\endgroup$ –
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