I'm working with a set of $M$ vectors $ \{\mathbf{w}_i \in \mathbb{R}^N, \, i = 1, \ldots, M \}$. Since single vectors are usually considered as column vectors, I'm defining a matrix
$$
\mathbf{W} = [\mathbf{w}_1, \ldots, \mathbf{w}_M] \in \mathbb{R}^{N \times M}
$$
by placing the vectors as matrix columns.
However, for some descriptions, I need to refer to the matrix rows.
Is there an elegant notation to refer to this matrix rows (preferably with less notation overhead)?
Best Answer
Since $W_{nm}$ is unambiguous for the $n$th row, $m$th col entry of $W$, I quite like the following notation of using a star, dot, or colon as a placeholder for the other dimension (similar to how dot or star can be used as omitted entries in a matrix):
From a programming perspective, this is similar to how in R we simply leave off the other dimension, writing
W[n,]
andW[,m]
, and in Numpy we use a colon to represent the entire other axis withW[n,:]
andW[m,:]
.