numpy (matrix solver) - python vs. matlab

Tue May 1 18:04:59 EDT 2012

On 5/1/2012 21:59, Colin J. Williams wrote:
> On 01/05/2012 2:43 PM, someone wrote:
> [snip]
>>> a = [1 2 3]; b = [11 12 13]; c = [21 22 23].
>>>>>> Then notice that c = 2*b - a. So c is linearly dependent on a and b.
>>> Geometrically this means the three vectors are in the same plane,
>>> so the matrix doesn't have an inverse.
>>>> Does it not mean that there are three parallel planes?

They're not parallel because our matrix has rank 2, not 1.
Anyway, have a look at this:
http://en.wikipedia.org/wiki/Parallelepiped#Volume
It follows that our matrix A whose rows are a, b and c represents a 
parallelepiped. If our vectors are collinear or coplanar, the 
parallelepiped is degenerate, i.e. has volume 0. The converse is also true.
Kiuhnm