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Imaginary Matrix Division
08-21-2021, 02:57 AM
Post: #1
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
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08-21-2021, 06:17 AM
Post: #2
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.

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08-21-2021, 06:43 AM
Post: #3
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.

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08-21-2021, 08:05 AM
Post: #4
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.

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08-21-2021, 09:29 AM (This post was last modified: 08-21-2021 09:30 AM by Werner.)
Post: #5
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

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08-21-2021, 11:21 AM (This post was last modified: 08-21-2021 11:26 AM by Albert Chan.)
Post: #6
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.

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08-21-2021, 01:29 PM
Post: #7
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

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08-22-2021, 05:22 PM
Post: #8
RE: Imaginary Matrix Division
Is there a reason to not support both left and right division of matrices?
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08-23-2021, 11:57 AM
Post: #9
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.
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08-23-2021, 05:30 PM
Post: #10
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.
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08-23-2021, 06:41 PM
Post: #11
RE: Imaginary Matrix Division
Can we get B*inv(A) without evaluating inverse and multiply ?
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08-24-2021, 05:19 AM
Post: #12
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

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