Re: Lists: Row Vectors vs. Column Vectors. (feels
- To: mathgroup at smc.vnet.net
- 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.
> 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
Prev by Date:
Re: Lists: Row Vectors vs. Column Vectors. (feels like such a silly
Next by Date:
Re: Workbench fails to build documentation
Previous by thread:
Re: Export 3D graphics to Web page (a la LiveGraphics3D)
Next by thread: