I am currently researching a QR-based root finding algorithm encountered two operations that I don't understand. I'd love to look them up, but I can't find the names of these operations/notations.
The first was an unfamiliar usage of a colons and commas in a possibly set related way - (1 : 2, 1). The term seemed to be expressed as the coefficient to another term (I.E. F(1 : 2, 1)). I later encountered a similar term (1 : 2, 2 : 3) that also seemed represented as a coefficient to a variable.
NOTE: After running a few more searches and rereading the article I encountered this on, I realized this notation may be matrix related rather than set related. F is actually a unitary matrix used to generate another matrix, it seems. I thought these might be matrix indices, but the typical notation for this used in the article is two comma separated subscript numbers.
Specifically, I encountered this in equation (21) under Theorem 2.8 of the paper A fast implicit QR eigenvalue algorithm for companion matrices. The equation describes a vector hk as the result of a formula Fk (1 : 2, 1) and a matrix Bk + 1 as the result of an equation Fk (1 : 2, 2 : 3).
The second is the one I had trouble running a search on. It seemed to be two terms, one over top of the other, in parenthesis as if functioning as a coefficient. I came up with the term "binomial coefficient" at some point, but I believe this might not be correct.
I'd settle for just the names of these two operations/notations, but if anyone is willing to explain what exactly they mean, it'd be appreciated. Thank you for taking the time to read this question. I apologize if this is not a suitable question for this forum or the details are inadequate.