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If I had a vector $\mathbf{x}$, I would denote element $i$ as $x_i$.

However, if my vector already has a subscript, for example $\mathbf{x}_j$ or $\mathbf{x}_{10}$, how should I show element $i$?

I would like to retain the information that the element comes from $\mathbf{x}_j$ (as opposed to for example $\mathbf{x}_k$).

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What I usually see is $(x_i)_j$ for the $j$-th element of $x_i$ (this is what I do). It's also quite common to write $x_{ij}$ as if the vectors are rows of a matrix.

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Great, this makes a lot of sense to me, thanks. – Bill Cheatham Apr 22 '13 at 17:12
For sequences of vectors, I've recently seen the following: $x_i^{(k)}$ is the $i$th component of the $k$th vector in the sequence of vectors $\mathbf{x}^{(n)}$. – Todd Wilcox Apr 22 '13 at 17:30

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