Talk:Transfer matrix

Misleading title
I think that the title of this article is misleading. In standard control theory (see, e.g., books by Vidyasagar (1985), Francis (1987), Goodwin et al (2001), etc.) the term is used to refer to the relationship between Laplace transforms of the input and output of a multi-input multi-output system (MIMO). In other words, to the straightforward extension of the term transfer function to MIMO systems. In this article, the term is used in a very specific way.

I suggest to change the title accordingly. —Preceding unsigned comment added by Eisv (talk • contribs) --11:08, 24 September 2007

Dear IP/unkown, please yourself and create the article Transfer function (control theory). If this has been done, then one can think about further measures. Please consider that besides the great and all-embracing systems theory there are such minor topics such as wavelet theory, where related concepts get related names.--LutzL 11:48, 24 September 2007 (UTC)
 * Well I've now created transfer function matrix which I think is the suggested article, but under a different (more usual name). This article now has three hatnotes.  I think it is time to consider turning it into a dab.  I would certainly question whether the current article has the primary meaning. SpinningSpark 04:04, 25 December 2016 (UTC)


 * Title is still misleading. The generalization of a matrix is an operator, and transfer operator is the generic thing studied in math; but it has nothing to do with the contents here. This article seems to be describing something very specific, pertaining to wavelets only, and not at all that thing that is generally studied in physics, engineering and dynamical systems (and biology, when biologists get that deep...) I think the generic transfer matrix is studied a zillion-times more often than the thing described here... right? Would it be possible to have an article on the general idea of a transfer matrix, here? (More precisely, I am writing Draft:Resonant interaction and wanted to link here, by saying something like "The transfer matrix describes how the normal modes participating in the resonant interaction spread their energy around".  Something like that. The article on transfer function matrix is related-ish, but it is specific to control theory, and fails to mention that the transfer is generically bi-directional; things go any-which old way... that there is mixing involved, or that perturbation theory is involved...) To be clear: a generic transfer matrix is a transfer coefficient which is a matrix. 67.198.37.16 (talk) 20:10, 15 September 2020 (UTC)

Draft of correct definition of transfer matrix
Below is a very fast draft of what I believe the correct definition of a transfer matrix would need to say.

A transfer matrix is a matrix generalization of a transfer coefficient. Given normal modes $$a$$ and $$a^*$$, which are usually real or complex-valued functions of one or more variables $$k$$, the transfer matrix components are given by


 * $$T^{\pm\pm}_{\;\;\;mn}=\int a^\pm_{\;n}(k) V(k,q) a^\pm_{\;m}(q) dk dq$$

Note that informally, the $$a$$ and $$a^*$$ can be understood to correspond to the destruction and creation operators of a simple harmonic oscillator: that is, they create or remove normal modes of the system under study. It is usually the case that $$V(k,q)$$ is diagonal, e.g. in the case of resonant interactions.

Something like that. I don't have a reference book in my lap; above is a mash-up of what I see when I read papers that use it. p.s. I would not be at all surprised if the wavelet-thingy is exactly the above, with the $$a_n$$ being the wavelets, and the shifted-over-by-two pseudo-diagonal form of the wavelet matrix is because ... well, however it is that wavelets decompose (they're cubics, right?) so the wavelet-thingy is a special case example of the general thing. I think the control-theory thing can also fit into this generic definition, right? and of course, the transfer-matrix-in-optics fits into this generic framework... 67.198.37.16 (talk) 21:04, 15 September 2020 (UTC)