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Example

Denote numpy.add by \(\stackrel{?}{+}\) and let

\begin{align*} A = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix}, \quad \vec{v} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}; \end{align*}

then

\begin{align*} A \stackrel{?}{+} \vec{v} & = A + 1 \vec{v}^{\mathsf{T}} \\ & = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix} + \vec{1} {\begin{pmatrix} 1 \\ 2 \end{pmatrix}}^{\!\!\mathsf{T}} \\ & = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix} + \begin{pmatrix} 1 \\ 1 \end{pmatrix} \begin{pmatrix} 1 & 2 \end{pmatrix} \\ & = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix} + \begin{pmatrix} 1 \\ 1 \end{pmatrix} \begin{pmatrix} 1 & 2 \end{pmatrix} \\ & = \begin{pmatrix} 100 & 200 \\ 300 & 400 \end{pmatrix} + \begin{pmatrix} 1 & 2 \\ 1 & 2 \end{pmatrix} \\ & = \begin{pmatrix} 101 & 202 \\ 301 & 402 \end{pmatrix} \end{align*}

and

import numpy as np
a = np.array([[100, 200], [300, 400]])
v = np.array([1, 2])
a + v

array([[101, 202],
       [301, 402]])