Given three $3D$ points: $A,B$ and $C$, what is the procedure to check if they are collinear?
In general, given $n$ points in $m$-dimension, how should one find out, if these $n$-points defines a hyperplane of dimension $m'$, where $m' \lt m$. And what should be the relationship between $n$ and $m$, if we are looking for hyperplanes of strictly smaller dimension.
And is there any general/efficient way in MatLab, to find this?
subtract one point from every other point to get $n-1$ vectors. Then put these vectors as columns into a matrix and compute the rank of the matrix (e.g. in Matlab), and this is the dimension of the hyperplane the points lie on.