Re: any deep thinking on why linear systems are commutative?

From: Number 6 (No6_at_distant.island.nz)
Date: 11/13/04 

Date: Sat, 13 Nov 2004 13:23:52 +1300

"Gordon Sande" <g.sande@worldnet.att.net> wrote in message
news:5fcfd.579$9b.372@edtnps84...
>
>
> kiki wrote:
> > Dear all,
> >
> > Could you please help me understand better by providing some deep
thoughts
> > on why linear systems are commutative?
> >
> > If T1 and T2 are linear systems, then y1=T2(T1(x)) and y2=T1(T2(x))
> >
> > y1 and y2 are the same.
> >
> > After seeing some examples of non-linear system and linear systems. I
got
> > convinced that for non-linear system this property does not hold.
> >
> > But any deeper thinking? Proof?
> >
> > Thanks a lot!
> >
>
> To answer the subject line: Composition of linear (time invariant)
> systems is convolution of their impulse responses. Now you can
> prove that, including the commuting part in passing, various ways
> so it is true for ALL LTI systems.

But not multiple input-output systems.

Tom

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