Imaginary Matrix Division
08-21-2021, 02:57 AM
Post: #1
 toml_12953 Senior Member Posts: 2,040 Joined: Dec 2013
Imaginary Matrix Division
The Prime does this:

[[1 1][1 1]] / [[1 1][1 i]]

[[1 1][0 0]]

Most other calculators get [[1 0][1 0]] for an answer. Which is right?

Tom L
Cui bono?
08-21-2021, 06:17 AM
Post: #2
 Joe Horn Senior Member Posts: 1,972 Joined: Dec 2013
RE: Imaginary Matrix Division
(08-21-2021 02:57 AM)toml_12953 Wrote:  The Prime does this:

[[1 1][1 1]] / [[1 1][1 i]]

[[1 1][0 0]]

Most other calculators get [[1 0][1 0]] for an answer. Which is right?

The 50g also gets [[1 1][0 0]].

Wolfram Alpha returns [[1 1][1 -i]]. Hmmm.

<0|ɸ|0>
-Joe-
08-21-2021, 06:43 AM
Post: #3
 Tonig00 Member Posts: 55 Joined: May 2016
RE: Imaginary Matrix Division
Interesting, matrix multiplication is not commutative.
If a = [[1 1][1 1]] and b = [[1 1][1 i]]
When ask Prime a/b gives a warning: inv(b)*a

This gives [[1 1][0 0]]

If you do a*inv(b) gives [[1 0][1 0]]

For me exponents should be operate first so prime in this misleading expresión is correct. But I am not sure, could be the opposite.

Toni
08-21-2021, 08:05 AM
Post: #4
 J-F Garnier Senior Member Posts: 845 Joined: Dec 2013
RE: Imaginary Matrix Division
(08-21-2021 06:17 AM)Joe Horn Wrote:
(08-21-2021 02:57 AM)toml_12953 Wrote:  The Prime does this:
[[1 1][1 1]] / [[1 1][1 i]]
[[1 1][0 0]]
Most other calculators get [[1 0][1 0]] for an answer. Which is right?
The 50g also gets [[1 1][0 0]].
Wolfram Alpha returns [[1 1][1 -i]]. Hmmm.

Same result, as early as the 28S, and even the HP-71B w/ Math ROM (doing INV(B)*A ).

(08-21-2021 06:43 AM)Tonig00 Wrote:  When ask Prime a/b gives a warning: inv(b)*a
This gives [[1 1][0 0]]
If you do a*inv(b) gives [[1 0][1 0]]
For me exponents should be operate first so prime in this misleading expresión is correct. But I am not sure, could be the opposite.

RPL machines (since the 28S) were implementing the "matrix division" a/b as inv(b)*a.

J-F
08-21-2021, 09:29 AM (This post was last modified: 08-21-2021 09:30 AM by Werner.)
Post: #5
 Werner Senior Member Posts: 803 Joined: Dec 2013
RE: Imaginary Matrix Division
(08-21-2021 06:17 AM)Joe Horn Wrote:  Wolfram Alpha returns [[1 1][1 -i]]. Hmmm.

That is the result of an element-wise division..
Matrix division being implemented as premultiplying by the inverse was already present in the 42S. Since [[1 1][1 1] has 2 identical colums, so will the result.

Cheers, Werner

41CV†,42S,48GX,49G,DM42,DM41X,17BII,15CE
08-21-2021, 11:21 AM (This post was last modified: 08-21-2021 11:26 AM by Albert Chan.)
Post: #6
 Albert Chan Senior Member Posts: 2,239 Joined: Jul 2018
RE: Imaginary Matrix Division
(08-21-2021 09:29 AM)Werner Wrote:  Matrix division being implemented as premultiplying by the inverse was already present in the 42S.

Matrix "division" B/A is really solving for A*X = B for X, without gettting inv(A)

It is faster and likely more accurate.

08-21-2021, 01:29 PM
Post: #7
 Werner Senior Member Posts: 803 Joined: Dec 2013
RE: Imaginary Matrix Division
(08-21-2021 11:21 AM)Albert Chan Wrote:  Matrix "division" B/A is really solving for A*X = B for X, without gettting inv(A)

Of course ;-) usually I’m the one telling others. I’m slipping..
Xheers, Werner

41CV†,42S,48GX,49G,DM42,DM41X,17BII,15CE
08-22-2021, 05:22 PM
Post: #8
 jte Member Posts: 222 Joined: Feb 2014
RE: Imaginary Matrix Division
Is there a reason to not support both left and right division of matrices?
08-23-2021, 11:57 AM
Post: #9
 roadrunner Senior Member Posts: 438 Joined: Jun 2015
RE: Imaginary Matrix Division
You would need a new symbol, perhaps B/A for left and B\A for right; but that may be more confusing than not supporting both.
08-23-2021, 05:30 PM
Post: #10
 jte Member Posts: 222 Joined: Feb 2014
RE: Imaginary Matrix Division
(08-23-2021 11:57 AM)roadrunner Wrote:  You would need a new symbol, perhaps B/A for left and B\A for right; but that may be more confusing than not supporting both.

In algebraic mode, there certainly could be a bit of confusion as to which is the dividend and which is the divisor in B\A (this wasn’t a problem in math classes I attended where left and right division were used on the blackboard due to relative vertical displacements). Issuing warnings when either are used could certainly be entirely reasonable.
08-23-2021, 06:41 PM
Post: #11
 Albert Chan Senior Member Posts: 2,239 Joined: Jul 2018
RE: Imaginary Matrix Division
Can we get B*inv(A) without evaluating inverse and multiply ?
08-24-2021, 05:19 AM
Post: #12
 Werner Senior Member Posts: 803 Joined: Dec 2013
RE: Imaginary Matrix Division
(08-23-2021 06:41 PM)Albert Chan Wrote:  Can we get B*inv(A) without evaluating inverse and multiply ?

Code:
 TRANS  X<>Y  TRANS  X<>Y  /  TRANS

Cheers, Werner

41CV†,42S,48GX,49G,DM42,DM41X,17BII,15CE
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