La multiplicación se define como:
\begin{equation} (AB)C \end{equation}Ejemplo 1:Multiplicar:
\begin{equation} \left [ \begin{matrix} 1 \\\ 2 \\\ 3 \end{matrix} \right ] \left [ \begin{matrix} 4 & 5 & 6 \end{matrix} \right ] \left [ \begin{matrix} 7 & 8 & 9 \end{matrix} \right ] \end{equation}Primero se multiplican $A$ y $B$:
\begin{equation} \left [ \begin{matrix} 1 \\\ 2 \\\ 3 \end{matrix} \right ] \left [ \begin{matrix} 4 & 5 & 6 \end{matrix} \right ] = \left [ \begin{matrix} 4 & 5 & 6 \\\ 8 & 10 & 12 \\\ 12 & 15 & 18 \end{matrix} \right ] \end{equation}Luego se multiplican todas las columnas de $AB$ con $C$.
\begin{equation} \left [ \begin{matrix} 4 \\\ 8 \\\ 12 \end{matrix} \right ] \left [ \begin{matrix} 7 & 8 & 9 \end{matrix} \right ] = \left [ \begin{matrix} 28 & 32 & 36 \\\ 56 & 64 & 72 \\\ 84 & 96 & 108 \end{matrix} \right ] \end{equation}\begin{equation} \left [ \begin{matrix} 5 \\\ 10 \\\ 15 \end{matrix} \right ] \left [ \begin{matrix} 7 & 8 & 9 \end{matrix} \right ] = \left [ \begin{matrix} 35 & 40 & 45 \\\ 70 & 80 & 90 \\\ 105 & 120 & 135 \end{matrix} \right ] \end{equation}\begin{equation} \left [ \begin{matrix} 6 \\\ 12 \\\ 18 \end{matrix} \right ] \left [ \begin{matrix} 7 & 8 & 9 \end{matrix} \right ] = \left [ \begin{matrix} 42 & 48 & 54 \\\ 84 & 96 & 108 \\\ 126 & 144 & 162 \end{matrix} \right ] \end{equation}El resultado es:
\begin{equation} \left [ \begin{matrix} 1 \\\ 2 \\\ 3\ \end{matrix} \right ] \left [ \begin{matrix} 4 & 5 & 6 \end{matrix} \right ] \left [ \begin{matrix} 7 & 8 & 9 \end{matrix} \right ] = \left [ \left [ \begin{matrix} 28 & 32 & 36 \\\ 56 & 64 & 72 \\\ 84 & 96 & 108 \end{matrix} \right ] \left [ \begin{matrix} 35 & 40 & 45 \\\ 70 & 80 & 90 \\\ 105 & 120 & 135 \end{matrix} \right ] \left [ \begin{matrix} 42 & 48 & 54 \\\ 84 & 96 & 108 \\\ 126 & 144 & 162 \end{matrix} \right ] \right ] \end{equation}
In [1]:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.text(1, 0, 0, "1", color='red')
ax.text(2, 0, 0, "2", color='red')
ax.text(3, 0, 0, "3", color='red')
ax.text(0, 1, 0, "4", color='blue')
ax.text(0, 2, 0, "5", color='blue')
ax.text(0, 3, 0, "6", color='blue')
ax.text(0, 0, 1, "7", color='green')
ax.text(0, 0, 2, "8", color='green')
ax.text(0, 0, 3, "9", color='green')
ax.set_xlim3d(0, 5)
ax.set_ylim3d(0, 5)
ax.set_zlim3d(0, 5)
ax.set_xlabel('Eje x')
ax.set_ylabel('Eje y')
ax.set_zlabel('Eje z')
ax.view_init(17, 24)
plt.show()
In [2]:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.text(1, 0, 0, "1", color='red')
ax.text(2, 0, 0, "2", color='red')
ax.text(3, 0, 0, "3", color='red')
ax.text(0, 1, 0, "4", color='blue')
ax.text(0, 2, 0, "5", color='blue')
ax.text(0, 3, 0, "6", color='blue')
ax.text(0, 0, 1, "7", color='green')
ax.text(0, 0, 2, "8", color='green')
ax.text(0, 0, 3, "9", color='green')
## 4 5 6
## 8 10 12
##12 15 18
ax.text(1, 1, 0, "4", color='magenta')
ax.text(2, 1, 0, "8", color='magenta')
ax.text(3, 1, 0, "12", color='magenta')
ax.text(1, 2, 0, "5", color='orange')
ax.text(2, 2, 0, "10", color='orange')
ax.text(3, 2, 0, "15", color='orange')
ax.text(1, 3, 0, "6", color='purple')
ax.text(2, 3, 0, "12", color='purple')
ax.text(3, 3, 0, "18", color='purple')
ax.set_xlim3d(0, 5)
ax.set_ylim3d(0, 5)
ax.set_zlim3d(0, 5)
ax.set_xlabel('Eje x')
ax.set_ylabel('Eje y')
ax.set_zlabel('Eje z')
ax.view_init(17, 24)
plt.show()
In [3]:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.text(1, 0, 0, "1", color='red')
ax.text(2, 0, 0, "2", color='red')
ax.text(3, 0, 0, "3", color='red')
ax.text(0, 1, 0, "4", color='blue')
ax.text(0, 2, 0, "5", color='blue')
ax.text(0, 3, 0, "6", color='blue')
ax.text(0, 0, 1, "7", color='green')
ax.text(0, 0, 2, "8", color='green')
ax.text(0, 0, 3, "9", color='green')
##28 32 36
##56 64 72
##84 96 108
##
## 35 40 45
## 70 80 90
##105 120 135
##
## 42 48 54
## 84 96 108
##126 144 162
ax.text(1, 1, 0, "28", color='magenta')
ax.text(2, 1, 0, "56", color='magenta')
ax.text(3, 1, 0, "84", color='magenta')
ax.text(1, 1, 1, "32", color='magenta')
ax.text(2, 1, 1, "64", color='magenta')
ax.text(3, 1, 1, "96", color='magenta')
ax.text(1, 1, 2, "36", color='magenta')
ax.text(2, 1, 2, "72", color='magenta')
ax.text(3, 1, 2, "108", color='magenta')
ax.text(1, 2, 0, "35", color='orange')
ax.text(2, 2, 0, "70", color='orange')
ax.text(3, 2, 0, "105", color='orange')
ax.text(1, 2, 1, "40", color='orange')
ax.text(2, 2, 1, "80", color='orange')
ax.text(3, 2, 1, "120", color='orange')
ax.text(1, 2, 2, "45", color='orange')
ax.text(2, 2, 2, "90", color='orange')
ax.text(3, 2, 2, "135", color='orange')
ax.text(1, 3, 0, "42", color='purple')
ax.text(2, 3, 0, "84", color='purple')
ax.text(3, 3, 0, "126", color='purple')
ax.text(1, 3, 1, "48", color='purple')
ax.text(2, 3, 1, "96", color='purple')
ax.text(3, 3, 1, "144", color='purple')
ax.text(1, 3, 2, "54", color='purple')
ax.text(2, 3, 2, "108", color='purple')
ax.text(3, 3, 2, "162", color='purple')
ax.set_xlim3d(0, 5)
ax.set_ylim3d(0, 5)
ax.set_zlim3d(0, 5)
ax.set_xlabel('Eje x')
ax.set_ylabel('Eje y')
ax.set_zlabel('Eje z')
ax.view_init(17, 24)
plt.show()