# 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.