What does the symbol X mean in the definition of the covariance matrix specifically?

Question

I just started to learn the covariance matrix in some machine learning online course. The following is the covariance matrix definition from the https://en.wikipedia.org/wiki/Covariance_matrix

I can see that the X are defined as the random variables in the column vector

From my understanding, it seems that the X is the vector. However, when I searched on the google , I found it seems that the X is the matrix. Each column of the matrix represents one observation and each row represents one dimension.

But when I checked on the wiki, there is no obvious explanation that the X is the matrix.

I would like to ask what the symbol X means in the definition of the covariance matrix specifically ? the vector or the matrix ? It should be a very basic problem but I can not get the point.

Thank you.

Answer 1

Here $X$ is a (column) random vector of length $n$. Then $XX^T$ is an $n\times n$ matrix, where $X^T$ is the transposed vector of $X$. The same holds for the mean vector $\mu_X$.