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Re: Lists: Row Vectors vs. Column Vectors. (feels

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  • Subject: [mg110529] Re: Lists: Row Vectors vs. Column Vectors. (feels
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Wed, 23 Jun 2010 01:53:43 -0400 (EDT)

Why stop at a special kind of Matrix object?  Why not a 3D array?  a 4D 
array? or higher-dimensional?

The root of the matter is that Mathematica simply does not have a 
general concept of an array of any number of dimensions, with automatic, 
corresponding display for the various dimensions.

This is unlike APL (and its successor, J), some of whose array-oriented 
approach has been carried over to Mathematica -- but, unfortunately, all 
grafted onto a single data structure, namely, lists.

I would be cautious about recommending a new type of object Matrix 
without revamping the foundation of Mathematica so as to handle 
arbitrary-dimension arrays as primitive objects.  But to do that would 
doubtless break a lot of user code!


On 6/22/2010 6:59 AM, telefunkenvf14 wrote:

> 'Vector' is a term used widely throughout mathematics and does not
> always have the same *intended* meaning. Ideally, to avoid confusion
> later on, we should teach matrix algebra by always referring to
> dimensions; a 1xn matrix, rather than calling it a row vector, and
> an mx1 matrix, rather than saying it's a 'column vector'.
>
> In general, a vector is just an ordered list of objects in some n
> space, such as R3, for example. *There's no reason to force such a
> concept into row or column form!*
> -----------
>
> Two remaining things I'd like to say:
>
> 1. I now feel a sense of frustration at the above lazy language in
> matrix algebra. It seems like a classic example where trying to make
> the material easier for a student to understand/visualize, actually
> ends up paving an intellectual cul-de-sac.
>
> 2. I'm still absolutely right about one thing: Mathematica needs to have a
> consistent way to programmatically create a matrix----that both
> *looks* like a matrix in StandardForm and *behaves* like one. What I
> mean is: On screen formatting and behavior just like Insert->Table/Matrix=92->=92 New=92->=92Matrix=92. It seems logical that such a function would
> have the head Matrix, given that it's conveniently available for use
> in Mathematica. Now, does anyone want to whip up a frontend token to do this,
> and pass it along to their favorite contact at WRI? :)
>
> I suppose a variant of Kevin's code would also work---BTW Kevin,
> thanks for teaching me the $Post trick.
>
> -RG
>
> PS - I also think Column[] should be ColumnForm (looks like there's
> some back and forth on this) and Row[] should be RowForm[]. Or, at the
> very least, let these definitions shadow one another, along with a
> hard-to-miss warning in the documentation about the Mathematica convention
> that xxxxForm[] is for formatting only. Not including 'Form' in Row[]
> and Column[] makes it too easy to gloss over their intended use.

-- 
Murray Eisenberg                     murrayeisenberg at gmail.com
80 Fearing Street                    phone 413 549-1020 (H)
Amherst, MA 01002-1912


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