Questions about handling of matrices by the DM42

Discussion around the Swiss Micros DM42 calculator.
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mcc
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Questions about handling of matrices by the DM42

Post by mcc » Fri Oct 02, 2020 8:04 pm

Hi,

Warning! I am by no means a mathmatician!

Regarding matrices:
In the alphabet 'x' is before 'y'.
'x' is the horizontal direction and 'y' is the vertical direction of elements of a matrix.
While entering the dimensions of a newly to be created matrix one puts its size in x-direction
into the X-register and its size in y-direction in the Y-register on the stack.


So far so nice. Logical and understandable. Even for me ;)

And then, entering the matrix editorm, it displays
1:1 <value>
in the first line and pushing -> steps to the next element in
x-direction.

But what catch my curiosity: Why are the coordinates in front of the
value of the very element are displayed
y:x <value> ?

x:y <value> would have been seemed more logical to me.
But there must be a reason for it - which?
Same kind of "unlogical setup":
'j' represents the position of an element in x-direction.
'i' represents the position of an element in y-direction.
Why not vice versa ('i'=>x, 'j'=>y), serveing the alphabetical order?
Is there a certain reason for it?

Cheers,
mcc
DM 42 - SN: 00373, Firmware release v.:3.16. / DMCP 3.20. as compiled by SwissMicros

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PierreMengisen
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Location: Neuchâtel CH

Re: Questions about handling of matrices by the DM42

Post by PierreMengisen » Fri Oct 02, 2020 9:25 pm

There is no correspondence between a system of representation in x:y coordinates and the positions in a matrix.
Mathematicians consider a matrix as an arrangement of objects in rows (first) and columns (second).
Indications are always given in this order by the subscripts i and j.
So by moving down in a matrix we increment the index i and by moving to the right we increment index j.
Your confusion comes from your belief in an x and y representation as in the vectorial plane.

greetings
Pierre
[TI59 with PC100C; TI-84 Plus CE-T; HP41CV with HP IL loop & 2*82161A DCD & 82162 TP; HP15C; HP28S; DM41; DM41L; DM42; DM41X]

Thomas Okken
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Re: Questions about handling of matrices by the DM42

Post by Thomas Okken » Fri Oct 02, 2020 9:29 pm

The way matrix indices are ordered, with the row index first and the column index second, follows established mathematical convention. For example, see the section "Two-dimensional arrays" under "In mathematics" at https://en.wikipedia.org/wiki/Index_notation

mcc
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Re: Questions about handling of matrices by the DM42

Post by mcc » Sat Oct 03, 2020 6:50 am

Hi,

thanks for the mathematical infos ...! Now it make more sense to me.

On the other hand: If it is "math speak" to think of a matrix
as an arrangement of "vertical vectors"...why does the matrix
editor fills a matrix "horizontal direction first" then?

Cheers!
mcc
DM 42 - SN: 00373, Firmware release v.:3.16. / DMCP 3.20. as compiled by SwissMicros

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Walter
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Re: Questions about handling of matrices by the DM42

Post by Walter » Sat Oct 03, 2020 7:36 am

mcc wrote:
Sat Oct 03, 2020 6:50 am
If it is "math speak" to think of a matrix as an arrangement of "vertical vectors"...why does the matrix editor fills a matrix "horizontal direction first" then?
I'd guess because most people read from left to right ... 8-)
DM42 SN: 00041 Beta
WP 43S running on this device

HP-35, HP-45, ..., HP-50, WP 34S, WP 31S, DM16L

Thomas Okken
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Re: Questions about handling of matrices by the DM42

Post by Thomas Okken » Sat Oct 03, 2020 7:39 am

You can think of a matrix as a collection of vertical vectors or as a collection of horizontal vectors. Both are equally valid. And the HP-42S matrix editor is likewise orientation-agnostic; if you want to fill a matrix column by column, just press ↓ after each entry instead of → ...

mcc
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Re: Questions about handling of matrices by the DM42

Post by mcc » Sat Oct 03, 2020 1:36 pm

...I thought at least mathmaticians read from top to bottom... ;)
DM 42 - SN: 00373, Firmware release v.:3.16. / DMCP 3.20. as compiled by SwissMicros

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PierreMengisen
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Re: Questions about handling of matrices by the DM42

Post by PierreMengisen » Sat Oct 03, 2020 2:52 pm

No, mathematicians read in n dimensions, where there is neither up nor down, neither here nor there, but all at once. They are poets of the infinite... :?
Pierre
[TI59 with PC100C; TI-84 Plus CE-T; HP41CV with HP IL loop & 2*82161A DCD & 82162 TP; HP15C; HP28S; DM41; DM41L; DM42; DM41X]

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