*I am using NumPy notation when discussing dimensions here.*

I am getting all turned around when switching between m and n to indicate dimensions of a vector or matrix.

For example, from the beginning of class, we talk about the “length of a training set” being represented by the variable m. I like this because it is consistent if the training set is a dimensional vector (m,) or a 2-dimensional matrix (m,n). But now and again I see an equation explaining a vector with this notation,

Note that a and b are vectors here where n-1 is indicating a Python code implementation where the shared 1-dimension of the vectors is (n,) or (n,1).

Am I missing something nuanced here?

- I know dimensions in NumPy will look something like, (m, n, ...) where each additional variable is another dimension of the same array.
- Sometimes vectors are represented with n instead of m in the context of the NumPy dimensions like, (n,) versus (m,).
- Even in the context of a vector \vec{x}, we access elements by indexing, e.g.,
`x[0]`

is the first element of \vec{x}, or in other terms, x^{(0)} is the first element of the same vector.