"There are some references to using tensor products to solve potential equations that go back to 1964. They involve inverting (division?) of a tensor product matrix. I had some of this in my thesis (1968) and is also on the book I wrote that came our around 1972. I only have one copy left (its pages are turning yellow with age). I can scan those pages if you like."
I suspect you and I are talking past each other. I am not talking about inverting a matrix, and I am not sure you are following the problem. I can only guess that you are responding to my prompt: "It is surprising that it took until the 90s for the problem to bite someone and for explicit algorithms to emerge." In case you are coming late to the thread, I am referring to factoring a square matrice M into pairs of square matrices (P, Q) such that P⊗Q = M. Is this what you are talking about? It appears that this problem, known as NKP, has only recently been considered. Maybe I'm wrong? To some extent, I am experiencing this thread like: [setting Egypt, 300 BC] Researcher: Hmm, does anyone know of an algorithm for finding whether or not a given number divides another given number? The Chorus: In Alexandria, a great number of people have put work into the problem, some use blocks and others pitchers of water. Researcher: Huh, it seems here, after consulting a colleague that a certain Euclid has found such an algorithm. It surprises me that for as long as we have had multiplication it is only recently that one of us has found a way to factor. Academic: Well, in my work, predating Euclid, I multiplied many numbers. What say you? Is this what we are doing?
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