Imaginary Matrix Division

[toml_12953]

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?

[Joe Horn]

(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.

[Tonig00]

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

[J-F Garnier]

(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

[Werner]

(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

[Albert Chan]

(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.

https://www.hpmuseum.org/forum/thread-14...#pid128492
https://www.hpmuseum.org/cgi-sys/cgiwrap...read=65551

[Werner]

(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

[jte]

Is there a reason to not support both left and right division of matrices?

[roadrunner]

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.

[jte]

(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.

[Albert Chan]

Can we get B*inv(A) without evaluating inverse and multiply ?

[Werner]

(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