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I understand $y_{ij}$ can be used to represent a cell in a matrix (i.e., the value in row $i$ and column $j$), particularly where the length of $j$ is equal for all $i$. I know it can also be used to index a vector $y_{i.}$ where each element is a vector indexed by $j$, and that this can permit different lengths of $j$ for each $i$.

  • What is the general name of this mathematical structure?
  • Should I think of it as a matrix, a vector of vectors, a long data frame (with one column for each index and one column for the value) or something else?
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    Just call it either an "entry" (scalar) or a "block" (general). It is useful to thing of a matrix either in terms of its entries or in terms of its blocks, depending on the application.2011-12-09
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    It usually goes under the name of [index notation](http://en.wikipedia.org/wiki/Index_notation)2011-12-09
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    I'm not sure why a name is important. Unless there is something particularly interesting about the entries, they're really just elements of the scalar field.2011-12-09
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    Thanks everyone. Your responses are helpful. My question probably reflects the fact that I'm a relative novice at mathematics. When reading journal articles in statistics, I get taken out of my comfort zone. I've seen a wide range of applications of index notation, and I was looking for some form of general guidance about the essence of this notation, and perhaps, how to think about it.2011-12-09

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