Home / NumPy / Matrix multiplication: linarg.matmul (@)
Worked example
Compute
\begin{align*} Y = A B = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} = \begin{pmatrix} \vec{y}_1 & \vec{y}_2 \end{pmatrix} = \begin{pmatrix} 19 & 22 \\ 43 & 50 \end{pmatrix} \end{align*}with
\begin{align*} \vec{y}_1 & = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 5 \\ 7 \end{pmatrix} = 5 \begin{pmatrix} 1 \\ 3 \end{pmatrix} + 7 \begin{pmatrix} 2 \\ 4 \end{pmatrix} = \begin{pmatrix} 5 \\ 15 \end{pmatrix} + \begin{pmatrix} 14 \\ 28 \end{pmatrix} = \begin{pmatrix} 19 \\ 43 \end{pmatrix} \\[1ex] \vec{y}_2 & = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 6 \\ 8 \end{pmatrix} = 6 \begin{pmatrix} 1 \\ 3 \end{pmatrix} + 8 \begin{pmatrix} 2 \\ 4 \end{pmatrix} = \begin{pmatrix} 6 \\ 18 \end{pmatrix} + \begin{pmatrix} 16 \\ 32 \end{pmatrix} = \begin{pmatrix} 22 \\ 50 \end{pmatrix} \end{align*}by
import numpy as np
A = np.array([[1, 2],
[3, 4]])
B = np.array([[5, 6],
[7, 8]])
A @ B
| 19 | 22 |
| 43 | 50 |