I was reading a slide from a course on principle component analysis, and the notation caused me some confusion. There is a data matrix X which is of dimension (n, d). So, the matrix has n rows, each of these row vectors represents a single data point, and d columns, each indicates a feature. However, later the author uses the notation $x_i (1 \leq i \leq n)$. This $x_i$ vector represents apparently a single data point too, but it's a column vector from the context. So what I want to know is that is this a convention that the lower case x always indicates a column vector, despite the fact that it actually a row vector when it's part of matrix upper case X?
Edit: corrected some typos