[Numpy-discussion] matrix default to column vector?
Charles R Harris
charlesr.harris at gmail.com
Sat Jun 6 14:03:38 EDT 2009
On Sat, Jun 6, 2009 at 9:29 AM, Alan G Isaac <aisaac at american.edu> wrote:
> On 6/6/2009 12:41 AM Charles R Harris apparently wrote:
> > Well, one could argue that. The x.T is a member of the dual, hence maps
> > vectors to the reals. Usually the reals aren't represented by 1x1
> > matrices. Just my [.02] cents.
>
> Of course that same perspective could
> lead you to argue that a M×N matrix
> is for mapping N vectors to M vectors,
> not for doing matrix multiplication.
>
> Matrix multiplication produces a
> matrix result **by definition**.
> Treating 1×1 matrices as equivalent
> to scalars is just a convenient anomaly
> in certain popular matrix-oriented
> languages.
>
So is eye(3)*(v.T*v) valid? If (v.T*v) is 1x1 you have incompatible
dimensions for the multiplication, whereas if it is a scalar you can
multiply eye(3) by it. The usual matrix algebra gets a bit confused here
because it isn't clear about the distinction between inner products and the
expression v.T*v which is typically used in it's place. I think the only
consistent way around this is to treat 1x1 matrices as scalars, which I
believe matlab does, but then the expression eye(3)*(v.T*v) isn't
associative and we lose some checks.
I don't think we can change the current matrix class, to do so would break
too much code. It would be nice to extend it with an explicit inner product,
but I can't think of any simple notation for it that python would parse.
Chuck
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