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+--- Thread: Imaginary Matrix Division (/thread-17375.html)
Imaginary Matrix Division - toml_12953 - 08-21-2021 02:57 AM
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?
RE: Imaginary Matrix Division - Joe Horn - 08-21-2021 06:17 AM
(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.
RE: Imaginary Matrix Division - Tonig00 - 08-21-2021 06:43 AM
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
RE: Imaginary Matrix Division - J-F Garnier - 08-21-2021 08:05 AM
(08-21-2021 06:17 AM)Joe Horn Wrote:(08-21-2021 02:57 AM)toml_12953 Wrote: The Prime does this:The 50g also gets [[1 1][0 0]].
[[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?
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
RE: Imaginary Matrix Division - Werner - 08-21-2021 09:29 AM
(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
RE: Imaginary Matrix Division - Albert Chan - 08-21-2021 11:21 AM
(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-14571-post-128492.html#pid128492
https://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv014.cgi?read=65551
RE: Imaginary Matrix Division - Werner - 08-21-2021 01:29 PM
(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
RE: Imaginary Matrix Division - jte - 08-22-2021 05:22 PM
Is there a reason to not support both left and right division of matrices?
RE: Imaginary Matrix Division - roadrunner - 08-23-2021 11:57 AM
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.
RE: Imaginary Matrix Division - jte - 08-23-2021 05:30 PM
(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.
RE: Imaginary Matrix Division - Albert Chan - 08-23-2021 06:41 PM
Can we get B*inv(A) without evaluating inverse and multiply ?
RE: Imaginary Matrix Division - Werner - 08-24-2021 05:19 AM
(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
/
TRANSCheers, Werner