py40. Matrix operations in Python

We can use numpy.matrix to create matrices, rather than numpy.array. With numpy.array, the * operation is element-wise multiplication. However, with numpy.matrix, the * operation is real matrix multiplication. With numpy.array, we can always do real matrix multiplication with numpy.dot function.

The function numpy.trace finds the trace of a matrix, which is the sum of the diagonal.

# ex40.py
from __future__ import division, print_function
import numpy as np
A = np.matrix([[1,5,1],[2,-1,6],[1,0,3]])
print('A = \n',A)
B = np.matrix([[2,3,0],[3,-1,7],[4,8,9]])
print('B = \n',B)
print('5*A-10*B+3*A*B =\n',5*A-10*B+3*A*B)
print('trace(A*B)=',np.trace(A*B))
print('trace(B*A)=',np.trace(B*A))

#    A = 
#     [[ 1  5  1]
#     [ 2 -1  6]
#     [ 1  0  3]]
#    B = 
#     [[ 2  3  0]
#     [ 3 -1  7]
#     [ 4  8  9]]
#    5*A-10*B+3*A*B =
#     [[ 48  13 137]
#     [ 55 170 101]
#     [  7   1   6]]
#    trace(A*B)= 103
#    trace(B*A)= 103