# Self-similar matrices? [closed]

Does anyone know anything about self-similar (infinite) matrices, with more or less fractal(-like) structure and admitting meaningful matrix-algebra operations?

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## closed as not a real question by Mariano Suárez-Alvarez♦, Reid Barton, Anton GeraschenkoJan 5 '10 at 23:23

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.

Also, could the moderators or/and high-reputation users kindly add here a tag "fractals" or something like that? –  Igor Korepanov Jan 4 '10 at 12:45
How are they "self-similar" or "fractal"? What Hilbert space are these operators acting on? –  john mangual Jan 4 '10 at 12:47
Well, John, give me some time to think how to explain this... Or, in the case if you can read some Russian, here are two short texts with examples of such matrices: csc.ac.ru/ej/file/4381 and csc.ac.ru/ej/file/4641 . And thanks to Dmitri for creating the fractals tag! –  Igor Korepanov Jan 4 '10 at 13:29
This question should be closed, I think. If you can turn it into something more concrete with maybe a motivation and a small explanation, then I would be quite interested in reading it! As it stands, the answer is probably yes, as apparently someone knows something about that kind of matrices. –  Mariano Suárez-Alvarez Jan 4 '10 at 19:22
"nobody could say anything" perhaps because the question was too vague? Maybe they even had some information you're looking for, but they had no way to know it! –  Reid Barton Jan 5 '10 at 22:41

(here M_k is the k by k matrices over $\mathbb{C}$) where each inclusion is given by tensoring with the identity matrix in M_2. Every 'finite' element is "self-similar" in a sense.