[Jprogramming] The word for arrays of rank > 2

[Roger Hui]

Donald McIntyre, *Language as an intellectual tool: From hieroglyphics to
APL, *IBM Systems Journal, Volume 30, Number 4, 1991, page 569:

In 1848 Cayley showed that the combined effect of two rotations could be
represented as the product of two quaternions, and shortly afterwards
Sylvester (in the year he introduced the term *matrix*) pointed out that any
number of rotations can be represented by a single rotation about one axis.
As we would now say: each rotation can be represented by a matrix, and the
product of these matrices is a matrix completely describing the combined
rotation, whose axis is an eigenvector of this matrix, and the angle of
rotation can be found from the corresponding eigenvalue.  By 1855 Cayley
used matrix product (calling it the *composition* of matrices), and in his
memoir of 1858 he wrote: "It will be seen that matrices comport themselves
as single quantities; they may be added, multiplied, or compounded together,
etc.: the law of addition of matrices is precisely similar to that for the
addition or ordinary algebraical quantities; as regards their multiplication
(or composition), there is the peculiarity that matrices are not in general
convertible; it is nevertheless possible to form the poewrs (positive or
negative, integral or fractional) of a matrix ..." [17]  In this memoir he
uses Sylvester's latent roots (eigenvalues), but without naming them.

[17] A. Cayley, "A Memoir on the Theory of Matrices", Royal Society of
London, *Philosophical Transactions **148*, 17-37 (1858). Reprinted in
*Collected
Mathematical Papers **2*, No. 152 (1889).



On Tue, Oct 25, 2011 at 5:42 PM,  <simon at superware.com.au> wrote:
> According to this source, you're right.
>
> http://www.etymonline.com/index.php?term=matrix
>
> S
>
>
> Quoting Devon McCormick <devonmcc at gmail.com>:
>
>> I believe I heard (maybe from Ken?) that matrix is from the Latin "Mater"
>> (mother) because of the various factorization methods that create smaller
>> matrixes from an original one.
>>
>> On Tue, Oct 25, 2011 at 6:15 PM, Alexander Mikhailov <avmich at yahoo.com
>wrote:
>>
>>>
>>>
>>> Having word "matrix" (where it came from?..) and tradition in J to name
>>> things with non-traditional names (verb, noun), I'd vote for orthotope.
>>> Unmistakeable, succinct.
>>>
>>>
>>>
>>> ----- Original Message -----
>>> From: Henry Rich <HenryHRich at nc.rr.com>
>>> To: Programming forum <programming at jsoftware.com>
>>> Cc:
>>> Sent: Sunday, October 23, 2011 7:10 PM
>>> Subject: [Jprogramming] The word for arrays of rank > 2
>>>
>>> 'cube' was suggested.  Raul objected that a cube should have all axes of
>>> equal length.
>>>
>>> 'cuboid' has been used in Ye Dic (in the description of ;.0).  According
>>> to Wikipedia a cuboid should have rank 3.  And the word seems strained.
>>>
>>> 'hyperrectangle' is used, but it's a fifty-cent word for a ten-cent
idea.
>>>
>>> A fancier word is 'orthotope'.  Great if you're a Greek scholar.
>>>
>>> Also, 'box', which would be perfect if we weren't using it already.
>>>
>>> How about 'brick'? or 'block'?
>>>
>>> I like 'brick', followed by 'cube'.
>>>
>>> Henry Rich
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>>>
>>
>>
>>
>> --
>> Devon McCormick, CFA
>> ^me^ at acm.
>> org is my
>> preferred e-mail
>> ----------------------------------------------------------------------
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>>
>
>
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