Importing and Using NumPy

NumPy provides essential matrix operations. To use its functions, import the library as follows:

import numpy as np  # Standard import with np prefix
from numpy import * # Alternative import for direct access

Creating Matrices

Create matrices from one or two-dimensional data:

>>> import numpy as np
>>> vec = np.array([4, 5, 6])
>>> mat_from_vec = np.matrix(vec)
>>> print(mat_from_vec)
matrix([[4, 5, 6]])
>>> print(mat_from_vec.shape)
(1, 3)

Common matrix creation methods:

>>> zero_mat = np.mat(np.zeros((2, 3)))  # 2x3 zero matrix
>>> ones_mat = np.mat(np.ones((3, 2), dtype=int))  # 3x2 integer ones
>>> rand_mat = np.mat(np.random.rand(3, 3))  # 3x3 random matrix
>>> diag_mat = np.mat(np.diag([7, 8, 9]))  # Diagonal matrix

Common Matrix Operations

Matrix Multiplication

>>> A = np.mat([2, 3])
>>> B = np.mat([[4], [5]])
>>> C = A * B
>>> print(C)
matrix([[23]])

Element-wise Multiplication

>>> X = np.mat([3, 4])
>>> Y = np.mat([5, 6])
>>> Z = np.multiply(X, Y)
>>> print(Z)
matrix([[15, 24]])

Matrix Inversion and Transposition

>>> M = np.mat([[2, 0], [0, 2]])
>>> M_inv = M.I  # Inverse
>>> M_trans = M.T  # Transpose

Matrix Statistics

>>> data = np.mat([[1, 2], [3, 4], [5, 6]])
>>> col_sum = data.sum(axis=0)  # Column sums
>>> row_max = data.max(axis=1)  # Row maximums
>>> global_min = data.min()     # Global minimum

Matrix Splitting and Combining

>>> base = np.mat(np.ones((2, 2)))
>>> extra = np.mat(np.eye(2))
>>> vertical_join = np.vstack((base, extra))  # Vertical concatenation
>>> horizontal_join = np.hstack((base, extra)) # Horizontal concatenation

Converting Between Matrices, Lists, and Arrays

Convert between different data structures:

>>> my_list = [[1, 2], [3, 4]]
>>> my_array = np.array(my_list)
>>> my_matrix = np.mat(my_list)
>>> back_to_list = my_matrix.tolist()

Note: One-dimensional conversions behave different:

>>> simple_list = [5, 6, 7]
>>> mat_version = np.mat(simple_list)
>>> converted_back = mat_version.tolist()  # Returns nested list [[5, 6, 7]]

Extract scalar values from 1x1 matrices:

>>> single_val_matrix = np.mat([9])
>>> scalar = single_val_matrix[0, 0]  # Extract as integer