Do the rows of the design matrix refer to the observations or predictors?

I attempt to understand the formulation of dictionary learning for this paper:

Both papers used the exact formulation in two different domains.

Based on my understanding, in common machine learning, we formulate our matrices, from vectors, as rows to be observations, columns to be predictors.

Given a matrix, $$A$$:

$$\begin{array}{lcccccc} & p_1 & p_2 & p_3 & p_4 & p_5 & \text { label } \\ o_1 & 1 & 2 & 3 & 4 & 1 & 1 \\ o_2 & 2 & 3 & 4 & 5 & 2 & 1 \\ o_3 & 3 & 4 & 5 & 6 & 2 & 0 \\ o_4 & 4 & 5 & 6 & 7 & 3 & 0 \end{array}$$

So, using a math notation and excluding the label, I can define this matrix, $$A = [o_1, o_2, o_3, o_4] ∈ R^{4×5}$$, as $$A = [{(1, 2, 3, 4, 1), (2, 3, 4, 5, 2), (3, 4, 5, 6, 2), (4, 5, 6, 7, 3)}]$$, and in numpy:

import numpy as np

A = np.array([[1, 2, 3, 4, 1],
[2, 3, 4, 5, 2],
[3, 4, 5, 6, 2],
[4, 5, 6, 7, 3]])

A.shape
# (4, 5)


Am I right?