3 ms·
It would be good to define a nullspace for the matrix and then show you can show the linear independence of the corresponding homogeneous system (of vectors if
by selimthegrim 4y ago
It would be good to define a nullspace for the matrix and then show you can show the linear independence of the corresponding homogeneous system (of vectors if you wish) by having a non-zero determinant implying there is no nontrivial solution. That (L.I.) of two basis functions can just be shown by taking their sum to be zero and taking the derivative of this equation as another equation to form a like system.
- graycat 4y agoAh, I left out a lot! But I included enough that you could extend to some relatively deep parts! But among what I omitted was determinants. So, I couldn't mention your points! To me the one easy approach to determinants is to say that they give a volume, and the volume is zero if and only if there is linear dependence.