Re: why are there [v e c t o r s] in Lisp?

[Pascal J. Bourguignon]

Aurélien Aptel <aurelien.aptel+emacs@gmail.com> writes:

> I'm just nitpicking, but:
> […]
> In pure linear algebra, "direction" and "position" are not defined for
> vectors. 

Well once you define dot-product, you have defined implicitely angles
and therefore direction.

    A⋅B = |A|×|B|×cos(∠AB)
    A⋅B/(|A|×|B|) = cos(∠AB)

    For a vector V and a base (In), 
    (cos(∠VIn))=(V⋅In/|V|) defines the direction of the vector V.

    If (In)=((δin)), then (V⋅In/|V|) = V/|V|
    which shows that any vector defines a direction by itself.

The essence of vector is to define a direction and a magnitude.  Notably
for vector spaces without a finite basis, V/|V| is still the direction
of the vector V, intrinsically (every unitary vector is a distinct
direction).

-- 
__Pascal Bourguignon__                 http://www.informatimago.com/
“The factory of the future will have only two employees, a man and a
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