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MathGroup Archive 1998

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RE: Re: Re: Non-comm

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13414] RE: [mg13344] Re: [mg13280] Re: Non-comm
  • From: Ersek_Ted%PAX1A at mr.nawcad.navy.mil
  • Date: Thu, 23 Jul 1998 03:33:00 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Isn't this built-in as a different type of multiplication?

In[5]:=
?NonCommutativeMultiply

"a ** b ** c is a general associative, but non-commutative, form of \
multiplication."

If you like you can use the Notation package to define a convention for
Input and/or Output that is more readable.


Ted Ersek

|
|It's OK to say that we should not remove attributes from fundemantal
ops |like Plus and Times.  I agree, though for experimental purposes, I
like |the flexibility.  Thanks for giving us that. |
|However there is one obvious and common case where the Orderless
|attribute doesn't apply, namely matrix math.  The operation of
|multiplying matrices must not have the Orderless attribute. |
|Try writing out some matrix equations in Mathematica and asking the
|program to simplify or otherwise rearrange them.  Unless you have
|actually constructed the matrices symbolically, it won't work.  In
|other words, Mathematica does not allow any kind of shorthand for
|matrix math.  You have to write out {{a[1,1],a[1,2]},{a[2,1],a[2,2]}}
|and can't just put A.
|
|There is one, and only one definition for a new symbol like "A":  it
is, |by decree of Wolfram Research (:-/), a complex number.  It can't
be a |real number, an integer, or -- a matrix. |
|In the field of control theory, the whole point of using matrix math is
|the shorthand notation, thus:
|
|    x-dot = A.x + B.u  (system state equation) |    y     = C.x + D.u 
(system output equation) |
|where
|
|    x = the n x 1 state vector for
|              an nth-order system
|    u = the m x 1 input vector for
|              a system with m inputs |    y = the p x 1 output vector
for |              a system with p outputs |    A = the n x n system
(or plant) matrix for an |              nth-order system
|    B = the n x m input matrix for an |              nth-order system
with m inputs |    C = the p x n output matrix for an |             
nth-order system with p outputs |    D = the p x m feed forward matrix
for a |              system with p outputs and m inputs |
|In the past I tried to tinker with some Kalman filtering equations in
|Mathematica but got nowhere fast.  The Kalman theory is derived from
|pure symbolic matrix mathematics.  The dimensions of the matrices are
|irrelevant to the theory, but the fact that they are matrices is
|central.
|
|Sometimes you know the values of m,n,p but even in that case, in
|Mathematica you still have to write out the full matrices by hand.  At
|other times, you want to leave m,n,p undefined. |
|I would say that WRI should take the task of writing the rule base for
|symbolic matrix math with the Orderless attribute removed.  That's not
|a job for the users.  I think that this example alone answers David
|Withoff's proposition:
|
|> A separate question is whether or not functions such as Expand could
or |> should somehow be modified, probably by invoking separate
algorithms, |> to handle operations in other algebras.  That is an
interesting |> question, and one that many people have considered. |
|Yes, they should invoke separate algorithms for symbols declared as
|matrices, once we can make such declarations. |
|
|Best regards to the developers,
|
|Mark
|
|



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