Matrix indices

It's common to write the entries of a matrix \(A\) as \(a_{ij}\) without a comma:

\(A = \left(\begin{array}{cccc} a_{11}&a_{12}&\dots&a_{1n}\\ a_{21}&a_{22}&\dots&a_{nn}\\ \vdots&\vdots&\ddots&\vdots\\ a_{n1}&a_{n2}&\dots&a_{nn} \end{array}\right)\)

This is an exception to Juxtaposition means combine in the obvious way.

But it's also common to write the entries of a vector \(\mathbf{a}\) as \(a_i\):

\(\mathbf{a}=\left(\begin{array}{c}a_1\\a_2\\\vdots\\a_n\end{array}\right)\)

\(a_{12}\) could represent either the entry 1,2 in a matrix, or the 12th entry in a vector. \(a_{112}\) could represent a whole range of things.

This is perhaps most ambiguous for expressions like \(a_{2n}\) where we could be talking about the \(2n\)th entries in a vector or an entry in the 2nd row of a matrix.