🚀 go-pugleaf

In article <4g8b5i$irm@dfw.nkn.net>, TheAnalyst@Nfo.Org wrote:

> Now where the hell do you get "any ordered pair" from the above
definitions, or
> should I dig out my 8th grade linear algebra book :( don't ask why I
still have
> it ): .

> Just dug it out anyway.  NOWHERE is there a definition or is "vector" even
> listed.

Let me guess.  You didn't take math or computer science in university/college.
I wouldn't really assume that 8th grade (junior high!!)  linear algebra
would discuss more advanced than the concept of variables.  I don't even
think you would cover polynomial functions.  In fact, I wouldn't expect
functions and relations to be covered.

> Just did a little more research.  Guess what. . . "Vector" is not considered a
> part of "linear Algebra", it is a part of Physics and Calculus.  So unless you
> have an 8th grade education and that is where you stopped, your definition of
> "vector" is "a quantity requiring both magnitude and direction to be defined".

Considered by whom?  8th grade students?  This is bullsh*t.

True, a geometric vector may be a quantity requiring both magnitude and
direction.
However, in order to manipulate this  within the framework of an
n-dimensional vector space ,  you normally represent it as an n-tuple.

Very simple examples

Cartesian 1-dimensional:   [2], [3], [-2], [-500], etc.
Cartesian 2-dimensional:   [2,4], [6,-3], [-12,64], etc.    <-- this is
your ordered pair
Cartesian n-dimensional:   [a1,a2,a3,...,an], etc     <-- this is your n-tuple

These cartesian vectors are made of the coefficients to a linear
combination of vector components.
In other words your vector w=[3,4] could be written as  w=3i+4j
In a cartesian coordinate system, these components are usually orthogonal,
running along the coordinate axes.  The coefficients may be real or
complex, depending on the vector space.

A point is implicitly a vector.  It can be described as a displacement
from a reference point. 
For instance, if your point p=(5,2), then it could be rewritten p=[0,0]+[5,2]

A generic point can be decribed as a vector equation p = r + k (r1)
or as a Cartesian equation A(kn) + .... + B(k2) + C(k1) + D = 0

These vectors could be represented as n-tuples describing polar
coordinates, using n-1 angles and a length scalar.

This is only covers certain kinds of vectors, and is a gross simplification.
Eventually, you'll have the math to work with matrices and functions as
special kinds of vectors.