Shilov's Linear Algebra writes a matrix with two bars on each side rather than square brackets. I didn't find any mention of it with a quick Google search, and I can't see any other examples this double bar notation.

Does it mean something other than a matrix? Is it an older notation? Or is it something else?

Thank you

  • $\begingroup$ I think your interpretation of the notation is correct. Single bars, on the other hand, seem to denote a determinant. $\endgroup$ – Dylan Moreland Oct 10 '11 at 13:21
  • $\begingroup$ Yes, it's a matrix (he uses double bars where most other people would use parentheses or brackets). Look at the definition here. $\endgroup$ – J. M. is a poor mathematician Oct 10 '11 at 13:25

It looks like he means a matrix when he uses double bars:

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He uses the standard notation for a determinant, i.e. single bars:

enter image description here

I don't know if his notation for matrices was something that was common at the time he wrote the book, but I don't think it's popular now.

  • 2
    $\begingroup$ Perhaps it is (was?) a Russian thing? It's also used in Gantmacher's The Theory of Matrices, for example. $\endgroup$ – Hans Lundmark Oct 10 '11 at 13:33
  • $\begingroup$ Ah, that sounds like it could very well be the reason. $\endgroup$ – Zev Chonoles Oct 10 '11 at 13:40
  • $\begingroup$ Yeah, he made it clear that it was a matrix. But not being able to find a reference to the notation anywhere else was a bit disconcerting. Thanks! $\endgroup$ – Andrei Khramtsov Oct 10 '11 at 13:44

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