Computing with matrices and vectors

>>> import numpy as np
>>> A = np.array([[1, 2, 3], [4, 5, 6]]); print(A)
[[1 2 3]
 [4 5 6]]
>>> B = np.diag([1,2,3]); print(B)
[[1 0 0]
 [0 2 0]
 [0 0 3]]
>> At = np.transpose(A); print(At)  # transposed of A
[[1 4]
 [2 5]
 [3 6]]
>>> A.dot(B)       # matrix multiplication as method
array([[ 1,  4,  9],
       [ 4, 10, 18]])
>>> print( A @ B)  # matrix multiplication as operator
[[ 1  4  9]
 [ 4 10 18]]
>>> print(A @ At)
[[14 32]
 [32 77]]
>>> C = At @ A; print(C)
[[17 22 27]
 [22 29 36]
 [27 36 45]]
>>> print(C + B)   # addition of matrices
[[18 22 27]
 [22 31 36]
 [27 36 48]]
>>> print(3*A)     # scalar multiplication
[[ 3  6  9]
 [12 15 18]]
>>> v = np.array([[1],[2],[3]]); print(v)
[[1]
 [2]
 [3]]
>>> print(A @ v)   # matrix-vector multiplication
[[14]
 [32]]
>>> print(vt @ At) # vector-matrix multiplication
[[14]
[[14 32]]
>>>
>>> import numpy.linalg as la
>>> Bmat = matrix(B)           # change from array to matrix datastructure
>>> la.matrix_power(Bmat, 3)   # exponentiation:  B^3 = B @ B @ B
matrix([[ 1, 0,  0],
        [ 0, 8,  0],
        [ 0, 0, 27]])
>>> la.matrix_power(Bmat, -1)  # inverse as power
matrix([[1.     , 0.      , 0.        ],
        [0.     , 0.5     , 0.        ],
        [0.     , 0.      , 0.33333333]])
>>> la.inv(B)   # inverse array
array([[1.     , 0.      , 0.        ],
       [0.     , 0.5     , 0.        ],
       [0.     , 0.      , 0.33333333]])

Operations on matrix elements

>>> print(A)
[[1 2 3]
 [4 5 6]]
>>> print(A**2)
[[ 1  4  9]
 [16 25 36]]
>>> print(A*A)
[[ 1  4  9]
 [16 25 36]]
>>> print(A / A)
[[1. 1. 1.]
 [1. 1. 1.]]