## Questions about handling of matrices by the DM42

Discussion around the Swiss Micros DM42 calculator.
mcc
Posts: 233
Joined: Fri Jun 23, 2017 5:10 am

### Questions about handling of matrices by the DM42

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

PierreMengisen
Posts: 118
Joined: Wed Nov 29, 2017 1:38 pm
Location: Neuchâtel CH

### Re: Questions about handling of matrices by the DM42

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
Posts: 758
Joined: Tue May 02, 2017 5:48 pm
Location: United States
Contact:

### Re: Questions about handling of matrices by the DM42

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
Posts: 233
Joined: Fri Jun 23, 2017 5:10 am

### Re: Questions about handling of matrices by the DM42

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

Walter
Posts: 1611
Joined: Tue May 02, 2017 11:13 am
Location: Close to FRA, Germany

### Re: Questions about handling of matrices by the DM42

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 ...
DM42 SN: 00041 Beta
WP 43S running on this device

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

Thomas Okken
Posts: 758
Joined: Tue May 02, 2017 5:48 pm
Location: United States
Contact:

### Re: Questions about handling of matrices by the DM42

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
Posts: 233
Joined: Fri Jun 23, 2017 5:10 am

### Re: Questions about handling of matrices by the DM42

...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

PierreMengisen
Posts: 118
Joined: Wed Nov 29, 2017 1:38 pm
Location: Neuchâtel CH

### Re: Questions about handling of matrices by the DM42

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]