NUMPY ALGEBRA
In [1]:
#Dot Product
import numpy as np
a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
dot_product = np.dot(a, b)
print("Dot Product:", dot_product)
Dot Product: 32
In [2]:
#Matrix Multiplication
import numpy as np
matrix1 = np.array([[1, 2], [3, 4]])
matrix2 = np.array([[5, 6], [7, 8]])
matrix_product = np.matmul(matrix1, matrix2)
print("Matrix Product:\n", matrix_product)
Matrix Product: [[19 22] [43 50]]
In [3]:
#Determinant
import numpy as np
matrix = np.array([[1, 2], [3, 4]])
determinant = np.linalg.det(matrix)
print("Determinant:", determinant)
Determinant: -2.0000000000000004
In [4]:
#Inverse
import numpy as np
matrix = np.array([[1, 2], [3, 4]])
inverse_matrix = np.linalg.inv(matrix)
print("Inverse Matrix:\n", inverse_matrix)
Inverse Matrix: [[-2. 1. ] [ 1.5 -0.5]]
In [5]:
#Eigenvalues and Eigenvectors
import numpy as np
matrix = np.array([[1, 2], [2, 1]])
eigenvalues, eigenvectors = np.linalg.eig(matrix)
print("Eigenvalues:", eigenvalues)
print("Eigenvectors:\n", eigenvectors)
Eigenvalues: [ 3. -1.] Eigenvectors: [[ 0.70710678 -0.70710678] [ 0.70710678 0.70710678]]
In [6]:
#Solving Linear Equations
import numpy as np
A = np.array([[3, 1], [1, 2]])
b = np.array([9, 8])
solution = np.linalg.solve(A, b)
print("Solution:", solution)
Solution: [2. 3.]
In [7]:
#Singular Value Decomposition (SVD)
import numpy as np
matrix = np.array([[1, 2, 3], [4, 5, 6]])
U, S, V = np.linalg.svd(matrix)
print("U Matrix:\n", U)
print("Singular Values:", S)
print("V Matrix:\n", V)
U Matrix: [[-0.3863177 0.92236578] [-0.92236578 -0.3863177 ]] Singular Values: [9.508032 0.77286964] V Matrix: [[-0.42866713 -0.56630692 -0.7039467 ] [-0.80596391 -0.11238241 0.58119908] [ 0.40824829 -0.81649658 0.40824829]]
In [8]:
#Trace (sum of diagonal elements)
import numpy as np
matrix = np.array([[1, 2], [3, 4]])
trace = np.trace(matrix)
print("Trace:", trace)
Trace: 5