B.4.A.sagews

from sympy import *

A = Matrix([
    [2, -1],
    [1,  0]
    ])

B = Matrix([
    [ 3, 2, -1],
    [-2, 0,  1]
    ])

C = Matrix([4, 3, -2]).transpose()

D = Matrix([3, -1, 2])

E = Matrix([
    [  3,  2],
    [ -1, -2],
    [  0,  1]
    ])

F=Matrix([
    [ 2, 0, -2],
    [ 1, 3,  2],
    [-2, 1,  0]
    ])

G = Matrix([4,1]).transpose()

H = Matrix([
    [0, -1],
    [1,  0]
    ])
nams = ["A", "B", "C", "D", "E", "F", "G", "H"]
mats = [A,B,C,D,E,F,G,H]
nm = zip(nams,mats)

for (n, m) in nm:
    print(n+" &= " +latex(m)+"\\\\")

for (n1, m1) in nm:
    print
    pprint(n1)
    for (n2, m2) in nm:
        try:
            prod = m1*m2
            pprint(n1+n2+" &= ")
            pprint(latex(prod)+"\\\\")
        except ShapeError:
            continue

A &= \left[\begin{matrix}2 & -1\\1 & 0\end{matrix}\right]\\ B &= \left[\begin{matrix}3 & 2 & -1\\-2 & 0 & 1\end{matrix}\right]\\ C &= \left[\begin{matrix}4 & 3 & -2\end{matrix}\right]\\ D &= \left[\begin{matrix}3\\-1\\2\end{matrix}\right]\\ E &= \left[\begin{matrix}3 & 2\\-1 & -2\\0 & 1\end{matrix}\right]\\ F &= \left[\begin{matrix}2 & 0 & -2\\1 & 3 & 2\\-2 & 1 & 0\end{matrix}\right]\\ G &= \left[\begin{matrix}4 & 1\end{matrix}\right]\\ H &= \left[\begin{matrix}0 & -1\\1 & 0\end{matrix}\right]\\ A AA &= \left[\begin{matrix}3 & -2\\2 & -1\end{matrix}\right]\\ AB &= \left[\begin{matrix}8 & 4 & -3\\3 & 2 & -1\end{matrix}\right]\\ AH &= \left[\begin{matrix}-1 & -2\\0 & -1\end{matrix}\right]\\ B BD &= \left[\begin{matrix}5\\-4\end{matrix}\right]\\ BE &= \left[\begin{matrix}7 & 1\\-6 & -3\end{matrix}\right]\\ BF &= \left[\begin{matrix}10 & 5 & -2\\-6 & 1 & 4\end{matrix}\right]\\ C CD &= \left[\begin{matrix}5\end{matrix}\right]\\ CE &= \left[\begin{matrix}9 & 0\end{matrix}\right]\\ CF &= \left[\begin{matrix}15 & 7 & -2\end{matrix}\right]\\ D DC &= \left[\begin{matrix}12 & 9 & -6\\-4 & -3 & 2\\8 & 6 & -4\end{matrix}\right]\\ DG &= \left[\begin{matrix}12 & 3\\-4 & -1\\8 & 2\end{matrix}\right]\\ E EA &= \left[\begin{matrix}8 & -3\\-4 & 1\\1 & 0\end{matrix}\right]\\ EB &= \left[\begin{matrix}5 & 6 & -1\\1 & -2 & -1\\-2 & 0 & 1\end{matrix}\right]\\ EH &= \left[\begin{matrix}2 & -3\\-2 & 1\\1 & 0\end{matrix}\right]\\ F FD &= \left[\begin{matrix}2\\4\\-7\end{matrix}\right]\\ FE &= \left[\begin{matrix}6 & 2\\0 & -2\\-7 & -6\end{matrix}\right]\\ FF &= \left[\begin{matrix}8 & -2 & -4\\1 & 11 & 4\\-3 & 3 & 6\end{matrix}\right]\\ G GA &= \left[\begin{matrix}9 & -4\end{matrix}\right]\\ GB &= \left[\begin{matrix}10 & 8 & -3\end{matrix}\right]\\ GH &= \left[\begin{matrix}1 & -4\end{matrix}\right]\\ H HA &= \left[\begin{matrix}-1 & 0\\2 & -1\end{matrix}\right]\\ HB &= \left[\begin{matrix}2 & 0 & -1\\3 & 2 & -1\end{matrix}\right]\\ HH &= \left[\begin{matrix}-1 & 0\\0 & -1\end{matrix}\right]\\